In a large bowl or the bowl of a stand mixer, dissolve the yeast and 1 teaspoon of sugar in the warm water. Let sit for 5-10 minutes, until bubbly and foamy. Add the butter, warm milk, egg, remaining ⅓ cup sugar, and salt to the yeast mixture.
Add 2 cups flour and mix until combined. Gradually add the remaining flour, ¼ cup at a time, until the dough is soft and slightly tacky but pulls away from the sides of the bowl. You may not need every bit of the flour, so stop once the dough reaches the right consistency.
Knead for 6 to 8 minutes, until the dough is smooth and elastic. The dough should still feel soft and slightly tacky, not dry. Shape the crescent dough into a ball. Place the dough in a greased bowl, cover, and let rise in a warm spot until doubled in size, about 1 hour.
After the dough has risen, gently punch it down and divide them into two balls. Roll each ball out into a circle that is about 12 inches wide, then cut each circle into twelve wedges using a pizza cutter.
Starting at the wide end of each triangle, roll the dough toward the pointed tip. Tuck the point underneath the roll, then gently curve the ends inward to form a crescent shape. Place on a lightly greased or parchment-lined baking sheet.
Cover the shaped rolls and let them rise until puffy and nearly doubled in size, about 30 to 60 minutes.
While the rolls rise, preheat the oven to 350°F. Bake for 10 to 12 minutes, until the rolls are puffed and lightly golden brown. Remove from the oven and immediately brush the warm tops with melted butter. Serve warm.