In a bowl or liquid measuring cup, sprinkle the yeast over the warm milk and let proof for about 5 minutes.
In the bowl of your stand mixer, whisk together the flour, sugar and salt.
Whisk the egg into the yeast mixture, then add to the dry ingredients. Use a wooden spoon to mix until it comes into a ball and then switch to a dough hook and knead until the dough pulls away cleanly from the sides.
Add the room temperature butter and continue to knead, about 10 minutes, until the dough reaches the windowpane stage – take a piece of dough about the size of a golf ball and stretch it out between your fingers and thumbs. If you can stretch it without the dough breaking, you’re good to go.
Transfer the dough to a lightly floured work surface and divide into three equal portions. Shape them into balls, then use a rolling pin and roll each ball into a long oval.
Sprinkle the cheddar evenly on the ovals, then roll up like a jelly roll. Place the rolls in a row in an 8″x4″ loaf pan.
Cover loosely with plastic wrap and let proof in warm place until doubled, up to 2 hours.
Preheat the oven to 340°F.
Brush with egg wash and scatter on extra cheese, as much as desired.
Bake for 45 minutes, tenting with foil if the top browns to quickly. Remove from oven, let cool for 10 minutes, then remove from the pan and let cool completely on a wire rack. Enjoy!
