Line a rimmed baking sheet with parchment paper or a silicone baking mat. Set aside.
In a small saucepan, stir milk, sugar, and 1/3 cup butter together. Heat over low heat just until butter melts and sugar dissolves. Cool to about 100-105 F.
Pour the milk mixture into the bowl of a stand mixer.
Add the yeast and warm water. Let stand for 5-10 minutes, or until yeast is foamy.
Add 2 cups flour and salt to yeast mixture. Using a dough hook, mix on low speed for about 1 minute.
With the mixer still going, add remaining flour, 1/2 cup at a time. Mix about 1 ½ minutes, or until dough starts to clean the sides of the bowl.
Knead on low speed for about 2 more minutes, or until dough is smooth and elastic – the dough will still be slightly sticky to the touch.
Place dough in a greased bowl, turning it to grease the top. Cover the dough with a clean, dry dish towel.
Let it rise in a warm place, free from draft, for about 15 minutes.
Turn the dough onto a lightly floured surface, and divide into 2 equal pieces.
On a lightly floured surface, roll one piece of dough a circle that’s about 9 inches in diameter.
Cut into dough into 8 pieces.
Roll each piece up, starting at the wide end.
Place on rimmed baking sheet lined with parchment paper or a silicone baking mat.
Repeat with remaining dough.
Cover the baking sheet with a dish towel, and let the dough rise for about 15 minutes.
Preheat oven to 400 F.
Bake for about 7-10 minutes, or until the rolls are golden brown.
Melt the remaining butter, and brush rolls with melted butter.
Rolls are best enjoyed while warm.