Melt butter with milk. Heat until very warm, but don't boil. Allow to cool to approximately 110 degrees F. Sprinkle yeast over the top, stir gently and allow to sit for 10 minutes.

Combine flour and salt.

In the bowl of an electric mixer, mix 1/3 cup sugar and eggs with paddle attachment until combined. Pour milk/ yeast mixture into egg mixture and stir to combine. Add half the flour and beat on medium speed until combined. Add the remaining flour and beat until combined.

Switch to the dough hook attachment and knead dough on medium speed for 10 minutes. If dough is too sticky, add 1/4 cup flour and beat 5 minutes longer.

Heat a metal or glass bowl so it's warm and drizzle a little vegetable oil. Place the dough in the bowl and toss to coat in oil. Cover the bowl with plastic wrap and set in a warm place for at least 2 hours until doubled.

Turn dough out onto the work surface. With a floured rolling pin, roll dough into a rectangle no wider than your loaf pan and about 20 inches long. Brush surface of dough with melted butter. Combine the 1 cup sugar with cinnamon. Sprinkle over dough. Starting at one of the short ends of the dough, roll the dough, keeping it tight. Peach seam to seal.

Grease loaf pan with softened butter. Place dough, seam side down into the pan. Cover with plastic wrap and allow to rise for 2 hours until doubled.

Preheat oven to 350 degrees.

Mix egg with a small amount of milk and brush over top of doubled loaf. Bake for 40 minutes on middle or lower rack in the oven.

Remove from oven and immediately remove from pan. Insert knife along edge to loosen and cool completely on wire rack.