Add the warm water, sugar, and instant yeast to a small bowl. Stir and leave for approximately 5 minutes, until lightly foamy.
Beat the egg in a separate small bowl.
Add the flour and salt to a large mixing bowl and stir to combine.
Pour in the yeast mixture, warm milk, beaten egg, and 3 tablespoons of melted butter.
Mix until a rough, shaggy dough forms.
Transfer the dough to a lightly floured surface and knead for 8 to 10 minutes, until smooth and elastic.
Add additional flour only one tablespoon at a time when the dough is too wet to handle. It should remain slightly tacky.
Place the dough in a lightly greased bowl and turn it once to coat the surface.
Cover and leave in a warm place for 60 to 90 minutes, or until approximately doubled in size.
Gently press the air from the risen dough.
Divide the dough into five equal portions and shape each portion into a smooth ball.
Cover the dough balls and let them rest for 10 to 15 minutes.
Flatten one ball into a round approximately 5 inches wide.
Place about ⅓ cup shredded mozzarella in the center, leaving a clean border around the edge.
Bring the edges of the dough over the cheese and pinch firmly to seal.
Turn the filled dough seam-side down and gently roll it into a 7- to 8-inch round. Avoid pressing hard enough to tear the surface.
Preheat a heavy skillet over medium to medium-high heat.
Place the naan in the dry skillet and cook for 2 to 3 minutes, until bubbles form and the underside develops golden brown spots.
Flip and cook the second side for another 2 minutes, or until the dough is cooked and the cheese has melted.
Adjust the heat as necessary so the outside does not burn before the center cooks.
Transfer the naan to a cooling rack or plate.
Brush immediately with some of the remaining melted butter.
Sprinkle with black sesame seeds or nigella seeds, when desired.
Repeat with the remaining dough and cheese.
Serve the cheese naan warm.