Mix the Dough: In a large mixing bowl, combine the all-purpose flour, instant yeast, sugar, and salt. Pour in the melted butter, warm milk, and the whisked egg. Stir everything together until it forms a soft, sticky, slightly wet dough.
Shape into a Ball: Turn the dough out onto a clean counter. Sprinkle a tiny bit of extra flour if needed so it doesn't stick to your hands. Gently fold the dough inward with your fingers a few times, pressing it down until it naturally shapes into a smooth ball.
The First Rise: Place your dough ball directly onto a lined baking sheet or a round pizza pan. Cover it with a clean kitchen towel and let it rest in a warm spot until it has almost doubled in size (about 30-40 minutes).
Flatten and Score: Once the dough has puffed up nicely, use the palms of your hands to gently flatten it out into a neat circle, roughly 23 cm in diameter. Take a very sharp kitchen knife or a blade and score deep lines across the dough in a grid/crisscross pattern.
Mix & Spread the Butter: In a small bowl, mix together the softened butter, minced garlic, chopped scallions, and salt until smooth. Spread this mixture evenly over the top of your scored dough. Use the back of a spoon to gently trace the cut lines again so they stay open.
Stuff with Cheese: Take your thick mozzarella slices and tuck them deep into all the crisscross cuts across the dough. Be generous! Brush the outer exposed edges of the dough with a little beaten egg if you want a shiny crust, and finish with a heavy pinch of fresh cracked black pepper over the top.
Bake to Perfection: Bake in a preheated oven at 200°C (400°F) using top-bottom heat for 20 to 25 minutes. Watch for the top to turn a deep golden brown and the cheese to bubble beautifully.
Serve Hot: Let it cool for just a minute or two on the pan so you don't burn yourself, then pull apart and enjoy while it's warm and stretchy!
