Prepare the yeast mixture by gently heating ½ cup of whole milk and ¼ cup of warm water to 110-115°F. Combine the milk-water blend with 2 tablespoons of granulated sugar in a bowl and sprinkle 2¼ teaspoons of active dry yeast over the top.

Mix the dough ingredients: In a large bowl, add 1 teaspoon of salt, 1 large egg, and 3½ cups of all-purpose flour to the yeast mixture. Mix in ¼ cup of softened unsalted butter and combine until a shaggy dough forms.

Knead the dough: Knead on low speed for about 8 minutes or by hand until smooth and slightly sticky.

First rise: Transfer the kneaded dough into a greased bowl, cover with a towel, and let it rise in a warm spot until doubled in size, about 30-60 minutes.

Shape the rolls: Punch down the dough and divide it into 15 equal pieces. Shape each piece into a ball and arrange in a greased baking dish.

Preheat and bake: Preheat your oven to 375°F while the rolls rise. Bake for 19-23 minutes until golden brown.

Finish with butter: Brush tops with melted butter as soon as they come out of the oven and let them cool slightly before serving.