Activate the yeast. In a small bowl, combine the warm milk and sugar. Sprinkle the yeast over the top and let it sit for 5 to 10 minutes until foamy. If the mixture does not foam, the yeast may be expired or the milk was too hot.

Mix the wet ingredients. In a large bowl, whisk the melted butter and egg until smooth. Add the foamy yeast mixture and stir gently to combine.

Add the dry ingredients. Add the flour and salt to the wet mixture. Stir with a wooden spoon until a shaggy dough forms. Turn the dough onto a lightly floured surface and knead for 6 to 8 minutes until smooth and elastic. The dough should feel tacky but not sticky.

First rise. Place the dough in a greased bowl, cover with a clean kitchen towel, and let it rise in a warm spot for 1 to 1.5 hours, or until doubled in size. A turned off oven with the light on works well.

Shape the rolls. Punch down the dough and divide it into 12 equal pieces. Roll each piece into a smooth ball and place them in a greased 9x13 inch baking pan, leaving a little space between each roll.

Second rise. Cover the pan loosely and let the rolls rise for 30 to 45 minutes. They should puff up and touch each other slightly.

Bake the rolls. Preheat the oven to 350 degrees F. Bake for 15 to 18 minutes, or until the tops are golden brown and the internal temperature reads about 190 degrees F.

Make the cinnamon butter. While the rolls bake, beat the softened butter, cinnamon, and vanilla together in a medium bowl with a hand mixer for 2 to 3 minutes until light and fluffy.

Serve warm. Brush the hot rolls with a little extra melted butter if desired, then serve immediately with the cinnamon butter on the side.