In a large mixing bowl or the bowl of a stand mixer, combine warm water, 1 teaspoon sugar, and yeast. Let stand until foamy, about 5 minutes.
In this order, add the remaining 1/4 cup of sugar, whole milk, butter, and eggs. Add 2 cups of flour and salt. Mix with the paddle attachment or a wooden spoon until well combined.
Switch to the dough hook and turn the mixer on low speed, or continue mixing by hand with the wooden spoon. Add the remaining flour ½ cup at a time, kneading until a soft dough ball forms and starts to pull away from the sides of the bowl, about 15 minutes.
Shape the dough into a ball and place in a large, lightly oiled bowl. Cover and let rise in a warm place until doubled in size, 45 minutes.
Gently punch down the risen dough and divide it in half. On a lightly floured surface, shape each half into a ball and roll into a 12-inch circle. Using a pizza cutter or pastry wheel, cut the circle into 12 wedges.
Starting at the long edge, roll each wedge up to the point to form the crescent roll shape.
Line a baking sheet with parchment paper. Place crescent rolls on the baking sheet about 2 inches apart. Loosely cover and let rise until puffed, about 30 minutes.
Meanwhile, preheat the oven to 400F.
Bake for 10 to 12 minutes or until golden brown. Immediately brush with melted butter and serve warm.