Melt butter with milk. Heat until very warm, but don't boil. Allow to cool until still warm to the touch. Sprinkle yeast over the top, stir gently, and allow to sit for 10 minutes.
In another bowl, combine flour and salt.
In the bowl of an electric mixer, mix sugar and eggs with the paddle attachment until combined. Pour in the milk mixture and stir to combine. Add half the flour and beat on medium speed until combined. Add the other half and beat until combined.
Switch to the dough hook attachment and beat/knead dough on medium speed for ten minutes. If dough is overly sticky, add 1/4 cup flour and beat again for 5 minutes. Add more as needed.
Heat a glass mixing bowl so it's warm (I put mine in the oven and heated to 350, removed when it was done heating up or just before). Drizzle in a little canola oil, then toss the dough in the oil to coat. Cover bowl in plastic wrap and let rise for about 2 hours.
Melt 2 tablespoons of butter in a bowl. While it's melting, mix sugar and cinnamon together in another bowl.
Turn dough out onto the work surface. Roll into a rectangle no wider than the loaf pan you're going to use, and about 18 to 24 inches long. Smear with 2 tablespoons melted butter. Sprinkle the cinnamon sugar mix evenly over the butter-smeared dough.
Starting at the far end, roll dough toward you, keeping it tight and contained. Pinch seam to seal. Place dough, seam down, in the pan. Cover with plastic wrap and allow to rise for 2 hours.
Preheat oven to 350 degrees. Mix the egg with milk, and brush over the top. Bake for 40 minutes in the over.
Remove from the oven and let cool for a few minutes before removing from the pan. Allow bread to cool until warm or room temperature - slice and enjoy!