Activate the Yeast: In a large bowl, combine the warm milk, sugar, and yeast. Let it sit for about 5–10 minutes until it becomes highly frothy and bubbly.
Mix the Dough: Add the melted butter, egg, salt, and exactly 2 cups of the flour to the yeast mixture. Mix until well combined. Gradually add the remaining flour until a soft dough forms that pulls away smoothly from the sides of the bowl.
Knead: Turn the dough out onto a lightly floured surface. Knead for about 5–7 minutes until the dough is completely smooth and elastic.
First Rise: Place the kneaded dough in a lightly greased bowl, cover it with a damp cloth or plastic wrap, and let it rise in a warm spot for 1 hour (or until it has doubled in size).
Shape and Fill: Punch the risen dough down to deflate it and roll it out into a large rectangle on a clean surface. Sprinkle the shredded cheddar cheese evenly over the entire surface. Roll the dough up tightly into a long log and slice it evenly into 12 rolls.
Second Rise: Place the sliced rolls cut-side up in a greased 9×13 baking dish. Cover the dish loosely and let the rolls rise for another 30 minutes.
Bake: Preheat your oven to 375°F (190°C). Bake the proofed rolls for 20–25 minutes until the tops are golden brown and the cheese is beautifully bubbly.
Finish: In a small bowl, mix the 2 tablespoons of melted butter with the optional garlic powder. Brush the tops of the rolls generously with the garlic butter immediately after taking them out of the oven. Serve warm and enjoy!