In the bowl of a stand mixer, whisk together the warm water, yeast, and ¼ tsp sugar. Let sit for 5–10 minutes until foamy.
Add ⅓ cup sugar, warm milk, 5 tbsp softened butter, egg, and salt. Mix lightly — it's okay if the butter stays slightly separated.
Add 2 cups of flour and mix until well combined.
Switch to a dough hook and add the remaining 2½ cups flour. Knead for 4–5 minutes until the dough is smooth and elastic (slightly sticky is fine).
Transfer dough to a large greased bowl. Cover with greased plastic wrap and let rise in a warm, draft-free place until doubled in size, about 1½ hours.
Punch down the dough. Divide into two equal portions and shape each into a ball.
On a lightly floured surface, roll each ball into a circle about 35 cm / 14 inches wide. Spread each with about 2 tbsp softened butter.
Cut each circle into 12 wedges (like a pizza). Roll each wedge from the wide end to form crescents.
Place on baking sheets lined with parchment, with the tip tucked under.
Cover loosely with greased plastic wrap and let rise again for about 1 hour. Preheat oven to 375°F (190°C) during the last 15 minutes of rising.
Remove plastic wrap and bake rolls for 15–19 minutes, until golden brown. Brush with melted butter immediately after baking. Serve warm or allow to cool completely.