Set the oven to preheat at 375°F (190°C). Prepare a baking tray by lining it with parchment or coating lightly with oil.
In a medium skillet over medium heat, cook the ground beef together with the minced garlic until the meat is browned and fully cooked. Drain off any rendered fat.
Take the skillet off the heat, then stir in the chopped Parmesan and cubed cheddar until thoroughly combined and slightly melted.
Flatten each biscuit into a thin round using your hands or a rolling pin. Place a heaping tablespoon of the meat and cheese filling at the center of each dough circle. Fold the dough around the filling and pinch to secure the seams.
Arrange the sealed dough balls, seam side down, on the prepared tray. Brush the tops with the melted butter.
Bake in the center of the oven for 12 to 15 minutes, or until the biscuit exteriors are golden and baked through.
Allow to cool slightly before serving. Sprinkle with chopped parsley, if using.