In a small bowl, stir together the warm milk, sugar, and active dry yeast. Let it sit for 5–10 minutes until foamy.
In a large bowl, whisk together the flour and salt. Make a well in the center and add the yeast mixture, melted butter, and egg. Mix until a shaggy dough forms.
Turn the dough out onto a floured surface and knead for 8–10 minutes, until it's smooth and elastic.
Transfer the dough to a lightly greased bowl, cover with a clean kitchen towel, and let rise in a warm spot for about 1 hour, or until doubled in size.
Punch down the risen dough and divide it into 12 equal portions. Flatten each piece slightly, place about 1 tablespoon of shredded cheese in the center, and pinch the dough around it to seal and form a bun.
Place the buns seam-side down on a parchment-lined baking sheet. Cover loosely and let rise for another 30 minutes.
Preheat your oven to 375°F (190°C). For a golden top, brush each bun with a little milk or beaten egg before baking.
Bake for 15–20 minutes, or until the buns are golden brown and some cheese is just starting to peek out.
Let the buns cool for a few minutes before serving—best enjoyed warm while the cheese is still gooey!