Note: You will add in the flour in increments so pay close attention to the amount.
Combine 2 cups (270g) of flour, sugar, salt and yeast in a bowl of a stand mixer.
In a small saucepan, heat milk and water over the stovetop on low heat until 110°. It doesn't take long to warm up to the temperature so watch it closely.
With a paddle attachment, turn the mixer to low (1) and slowly add the liquid to the dry ingredients until it incorporates.
Add the egg and egg yolk still mixing on low speed.
Add one cup (136 grams) of flour until it is just incorporated and then switch to a dough hook.
Beat on medium speed (4) for one minute and then start adding the room temperature butter in slices to the dough. Wait until the butter is fully incorporated before adding the next butter slice.
On low speed (1), add the remaining 3/4 cup (104g) of flour to the dough.
Increase the speed back to medium (4) and continue to beat the dough for another 8 minutes. The dough will be sticky but should come off the sides of the bowl.
On a floured surface, knead the dough for another 2 minutes, dusting the surface again with flour when it becomes too sticky. The dough will be elastic and slightly sticky. Place dough into a well-greased bowl and cover with a towel or plastic wrap.
Let the dough rise for 1 hour or until it has doubled in size. Right before it has finished rising, begin making the filling.