Dissolve the yeast and 1 teaspoon of sugar in the warm water in a large bowl or the bowl of a stand mixer. Let sit 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 of flour, and mix until combined. Mix in additional flour, ¼ cup at a time, to form a soft dough that pulls away from the sides of the bowl.
Knead until smooth and elastic, about 6-8 minutes. Shape the dough into a ball, place in a greased bowl, cover, and let rise for about one hour, until doubled.
Gently punch down the dough after it has risen and divide 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.
Roll each wedge of dough up, starting at the wide end, to form a crescent shape. Place on a lightly greased or parchment lined baking sheet, cover, and let rise until doubled, 30-60 minutes.
Preheat the oven to 350°F while the dough is rising. Bake 10-12 minutes, until golden brown. Remove from the oven and brush with the melted butter. Serve warm.