In a small bowl or the bowl of a stand mixer, stir together 2 ¼ teaspoons yeast, 1 cup warm milk, and 1 tablespoon sugar. Let it sit for 5–10 minutes, until foamy.
Using a stand mixer with a dough hook attachment, add yeast mixture, 1 egg, 1 tablespoon sugar, ¼ cup butter, 1 teaspoon salt, and 1 cup all-purpose flour.
Mix on low for 30 seconds, then scrape down sides. Add the remaining 2 cups flour and mix on medium speed for 2–3 minutes, until a soft dough forms.
Turn the dough out onto a lightly floured surface and shape into a ball. Place in a lightly greased bowl, turning once to coat. Cover and let rise in a warm spot for 1–2 hours, or until doubled.
Punch down the dough and divide into 12 to 16 equal pieces. Shape into balls and arrange in a greased 9x13-inch baking dish or pan of your choice, spacing slightly apart.
Cover again and let rise for about 1 hour, or until rolls have puffed up.
Preheat oven to 350°F. Bake for 15–20 minutes, or until rolls are golden brown.
Remove from oven and immediately brush with softened butter. Serve warm.
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Notes
If the yeast doesn’t foam, toss it and try again with fresh yeast.
Cover the dough during rising to prevent it from drying out.
Don’t over-knead; it can make the rolls dense.
Use a cold (turned-off) oven as a draft-free place to rise the dough.