Mix flour, sugar, and salt in a large mixing bowl and make a well in the middle. Add the proofed yeast and mix using the hook of your standing mixer.
Add the egg and mix until dough is incorporated. Then add the water roux and try to mix until dough is incorporated .
Add the butter intermittently. Add a small amount of the butter, then mix, Add butter then mix, add the rest of the butter until you are able to form a smooth workable dough. Transfer the dough in an oil bowl and cover with cloth or plastic wrap and let rise in a warm place for an hour until it doubles its size.
When ready, punch the dough twice and work on it on a floured surface. Weigh the dough. The weigh of the dough here is 684 g and divide it by 12. So each dough is about 57 grams.
Form the dough into circle and arrange in a baking pan with 1/2 inch distance from each other. (please watch video on how you form the dough into round balls. Cover and let it sit in the warm place for thirty minutes. Preheat the oven at 350 F.
Place milk and egg in a small container and beat together to make an egg wash. Brush dough and bake.
Place oven rack in the middle and bake the dough in a preheated 350 F oven for 15-20 minutes. Or until top of the bread is golden brown.