This recipe uses a technique called tangzhong. It goes by several other names, such as hot water bread (or water roux bread), Hokkaido or Japanese milk bread and 65 degree bread (because you cook the roux to 65 degrees Celsius). The technique supposedly originated in Japan, but its popularity is widely attributed to Yvonne Chen, who wrote about it in a Chinese-language book. You'll probably be familiar with the bread, if not the technique, because it's what many Asian bakeries use to make those fluffy, slightly sweet rolls and loaves that stay soft for several days, instead of going hard quickly, thanks to the water roux (or, with this recipe, a milk roux) that helps the bread retain moisture.
It's not a difficult technique to master, and once you know how to do it, you can also use the basic dough recipe - omitting the cheese, and using plain butter - to make brioche-type loaves or rolls. If you can't find piment d’espelette butter in your supermarket, mix 200 grams (7oz) salted butter with about 3/4 tsp piment d’espelette, or another type of mild chilli powder.
It's important that you use the correct amount of flour to make the dough, so I've given weight measurements, rather than volume. If you don't use enough flour, the dough will be too soft.
This dough can be mixed and baked the same day, or refrigerated overnight, whichever is more convenient. The rolls are delicious on their own, but are even better when warmed then spread with even more butter.
Make the milk bread. Put the flour and milk in a saucepan, whisk until smooth then place the pan over a low-medium flame. Whisk constantly until an instant-read thermometer registers 65°C (150°F). Immediately remove the pan from the heat and set it aside to cool.
Heat the milk until you can see steam rising from the surface, either in a cup in the microwave or in a small saucepan on the stovetop. Cool until tepid. Divide the butter into two portions: put 50g (1¾oz) of the butter into a small pan (or a microwaveable cup) and set it aside. Cut the remaining butter into 1.5cm (⅔in) chunks and leave at room temperature until it's slightly pliable, but not melting. Grate the cheese on a fine-toothed rasp-type grater (such as a Microplane).
Put the bread flour and sugar into the bowl of a stand-type electric mixer and use a hand whisk to mix thoroughly. Add the yeast and whisk it in. Put the milk bread, milk and eggs into the bowl and immediately start mixing, using the dough hook. Mix on medium speed until the dough forms into a rough ball around the dough hook. Start adding the butter a chunk or two at a time, mixing until the butter is almost fully incorporated into the dough before adding more. The dough will be smooth but sticky. Turn the mixer speed to medium-high and beat for about five minutes, or until it passes the windowpane test: pull off a small lump of dough and roll it between the palms of your hands into a ball. Stretch the dough into a rectangle with your fingertips and thumbs. If it stretches so thin you can see light through it, it’s been kneaded enough; if the dough breaks and forms holes, continue to mix it.
When the dough is ready, add 50g (1¾oz) of the cheese and mix it until it’s just incorporated. Put the dough in a medium-sized bowl, cover with cling film and let it rise at room temperature until doubled. Remove the cling film and give the dough a firm punch with your fist to deflate it. Turn the dough over in the bowl, cover with cling film then refrigerate the dough until firm (about three hours, or you can refrigerate it overnight).
Melt the 50g (1¾oz) of butter you set aside, either in a microwave or on the stovetop.
On a lightly floured work surface, roll the dough into a 50cm x 35cm (20 x 14in) rectangle, dusting the dough with flour as needed so it doesn’t stick to the work surface or rolling pin.
Use the rolling pin to thin out one of the long sides of the rectangle. Use a pastry brush to dust away any excess flour on the surface of the dough. Brush some of the melted butter (not all of it) over the dough rectangle, but not the part that’s been thinned out. Sprinkle about 60g (2oz) of the grated cheese over the butter. Starting at the long end of the rectangle, roll the dough into a tight cylinder until you reach the thinned-out end. Lightly dampen that end of the rectangle with water and finish rolling the cylinder.Pinch the seam to seal it. Run your hands along the entire cylinder to stretch out the thicker parts and to make it as even as possible.
Measure the length of the cylinder, then cut it into 20 even pieces. Use pan-coating to spray large muffin tins (for individual rolls) or cake pans (for pull-apart bread). Place the rolls with a cut side up in the muffin tins or the cake pans (with the latter, leave 1cm (7/16in) between the pieces, so they have room to rise). Leave at room temperature until the pieces feel puffy.
While the rolls are rising, preheat the oven to 180°Celsius (350°F). Brush the tops of the dough with the remaining melted butter and sprinkle with the remaining cheese.
Bake at 180°C/350°F for about 40 minutes, or until done - they will be fragrant, medium-golden and firm to the touch, and will shrink slightly from the sides of the pan. Serve the rolls warm or at room temperature. Store leftovers in an air-tight container. If you want to keep the rolls for longer than three days, store them in the freezer. They can be reheated (thawed, if frozen) in a 180°C/350°F oven for about five minutes.