In a large bowl or the bowl of a stand mixer fitted with a paddle attachment, combine yeast with warm water. Stir, then let stand 5 minutes, until frothy. Add warm milk, melted butter and egg yolks and mix to combine. Add 2 cups of the flour, the sugar and salt. Switch to the kneading hook and mix until combined. Begin adding more flour, in small increments until a smooth, moist dough forms that cleanly pulls away from the bottom and sides of bowl, about 5 minutes. Remove to an oiled bowl and cover with plastic wrap to rise until doubled, about 1 hour.
Meanwhile, prepare filling by mixing butter with brown sugar and cinnamon in a small bowl until smooth. Set aside.
Grease a 9x5-inch loaf pan.
When dough has doubled, remove to a lightly floured surface and gently deflate. Divide dough in to 2 equal-sized pieces. Working with one piece, use a rolling pin to roll the dough in to a 9x14-inch rectangle. Spread half of the butter/brown sugar mixture evenly over the dough. With the short (9-inch) side facing you, roll the dough up jelly-roll style, pinching the seam together at the end. Place seam side down on one side of your prepared loaf pan. Repeat process with the second piece of dough, placing it next to the first roll in your loaf pan. Cover with a greased piece of plastic wrap and let rise until about doubled, about 45 minutes - 1 hour.
Preheat oven to 325° F. Prepare egg wash by whisking together egg and water. Brush on top of dough, being sure to get in the folds and down the exposed sides, as well.
Bake in preheated oven until deep golden, about 45-50 minutes. Check at 35 minutes or so and loosely cover with a piece of aluminum foil if top of bread is already dark enough. Continue cooking until 45 minutes or so. If you have an instant-read thermometer, bread should register around 200° F. when done.
Allow to cool in pan for 10 minutes, then run a knife around the edge and remove to a cooling rack to cool completely.