Heat griddle to about 400-425 degrees F.
Tear 2 slices of bread into small pieces and add to a large bowl. Or, you can grate the day-old bread to a finer consistency.
Add eggs, the ground meats, grated onion, ricotta, pecorino romano (or grated parmesan), basil, parsley, minced garlic, salt, and pepper to the bowl. Use your hands to combine all of the meatball ingredients thoroughly, but don't over-work the mixture.
Roll the meat mixture into individual meatballs that are equal in size. You can use a ¼ cup measuring cup to portion out the meat so that all of the balls are uniform. The balls should be medium-packed - if they are too loosely packed, they may fall apart when smashed on the griddle.
Add about 2 cups of marinara sauce to a small saucepan. Place the pan on the heated griddle to warm, stirring occasionally.
When the griddle reaches about 400-425 degrees F, place the meatballs down and allow them to start cooking for about 60-90 seconds. Then, flip the balls over to the other side. Use your spatula to gently press down on each meatball to flatten them out to about ½" thick and about the same width as your slider buns. *You don't want the meatballs to be too thin like a smash burger, because then they may fall apart on the griddle.
Allow the flattened meatballs to cook on the first side for about 4-5 minutes, or until a nice crust develops, then flip to the second side and continue to cook until the internal temperature reaches 160 degrees F.
While meatballs are cooking, add about 1-2 tablespoons of butter to a clear area on the griddle and spread the melted butter around with your spatula. Toast the slider buns cut side down in the butter until lightly golden brown, then remove from the griddle.
When meatball patties are just about done, top with about ½ slice of mozzarella cheese and about ¼ slice of provolone cheese. Allow the cheese to melt, then remove the cooked smashed meatballs from the griddle. You can use a melting dome if you wish.
Assemble the meatball sliders. Add a bit of warm marinara sauce to the top and bottom toasted buns. Sprinkle on some chopped basil for garnish. Add the smashed meatballs and serve warm.