Combine the warm milk, sugar, and yeast in a large bowl. Stir gently and let sit for about 5 minutes until slightly foamy.
Add the melted butter, egg, and salt to the yeast mixture. Gradually stir in the flour until a soft dough forms.
Turn out the dough onto a lightly floured surface and knead for about 8 to 10 minutes until smooth and elastic.
Place your dough in a greased bowl and cover it with a towel. Let it rise in a warm spot for 1 to 1½ hours or until doubled in size.
Punch down your dough gently to release air bubbles then transfer it back onto a floured surface. Roll or pat it into a rectangle about 8×14 inches. Sprinkle shredded cheese evenly over the surface.
Roll up the dough tightly from one short end and pinch the seam closed to seal. Place this seam-side down into a greased loaf pan. Cover again and let rise for another 30 to 45 minutes until puffy.
Preheat your oven to 350°F (175°C). Bake for about 30 to 35 minutes until golden brown on top and sounds hollow when tapped on the bottom.
Brush the top with melted butter for a glossy finish. Let your loaf cool in the pan for at least 15 minutes before slicing.