Preheat the oven to 375°F. Brush the bottom and sides of a 12-inch cast iron skillet or similar with melted butter. Set aside.
Beat together 6 large eggs with 3 Tbsp milk or cream. Season with salt and black pepper to your taste. Soft scramble then set aside to cool while you prepare the biscuit dough.
Use a fork to combine the self-rising flour and cream until the flour is fully moistened. It may appear crumbly but should hold together when pressed between your fingers.
Turn the dough out onto a lightly floured non-stick surface. Knead a few times until the dough comes together.
Flour a rolling pin and roll to around 1/4-inch thickness. Cut into 6-inch rounds. Re-roll scraps as needed to make 12 total.
Place 1/2 slice of cheese in the middle of the dough round, top with 2 Tbsp scrambled eggs, 1 Tbsp ham cubes and the other half slice cheese.
Pinch the dough around the filling. Place seam side down side by side in the skillet.
Brush the tops with melted butter them bake for 18 minutes at 375°F. Increase to 425°F and bake for another 5 minutes or until the tops are golden.
Serve immediately, brushed with additional butter, if desired