Preheat oven to 375 degrees F.
In a large bowl, combine the beef, pork, veal, egg, onion, parsley, garlic, oregano, salt, and pepper and mix until well combined. Scoop the mixture into mini muffin tins. Bake until browned, about 15 to 20 minutes. Serve on split biscuits with sauce and cheese.
Preheat oven to 400 degrees F.
In a large bowl, combine flour, 1/2 cup Parmesan, sugar, baking powder, salt, and pepper. Whisk until well blended. Add butter and combine with fingertips until a coarse meal forms. Mix in parsley. Gradually add milk, tossing with a fork until moist clumps form. Add extra milk if mixture is dry. Put dough on a floured work surface, folding 8 to 10 times until it becomes firm. Let rest for 10 minutes under a damp towel. Roll out on lightly floured work surface. Using a 2-inch-diameter biscuit ring, cut out biscuits and put on a parchment lined baking sheet. Sprinkle with remaining 1/2 cup cheese and bake until biscuits are puffed and golden, about 15 minutes.
In a medium pan over high heat, saute onion and garlic in olive oil until softened, about 3 minutes. Add tomatoes and allow to simmer until slightly reduced and thickened, about 25 minutes. Stir in fresh basil just before serving.