In the bowl of an electric stand mixer, fitted with the paddle attachment, add the bread flour, sugar, salt, yeast, milk and eggs. Beat until all the ingredients are combined.
Add the softened butter and beat until it’s incorporated.
Switch to the dough hook and on medium speed knead for 10-12 minutes. The dough should be smooth and pull away from the sides of the bowl.
Form the dough into a ball and place it into a buttered bowl,
Cover and allow the dough to rise until about doubled, or if you poke the dough with a floured finger it springs back slowly and leaves a small indentation.
Tip the dough out of the bowl onto a lightly floured surface.
Divide the dough into 16 pieces, approximately 32 grams each.
Flatten each piece of dough and gather up the sides and pinch together to form a ball.
Roll the balls under your cupped hand to smooth it and create tension.
Place the balls of dough in the prepared pan evenly spaced in a 4 x 4 pattern.
Cover with plastic and allow to rise until the rolls are just about touching each other and they are puffy. It may take anywhere from 1 hour – 1 ½ hours depending on the temperature.
Beat together 1 egg yolk and 1 teaspoon of water and brush over the tops of the risen rolls.
Bake in a preheated 350° F oven for 18 minutes