Heat a large cast-iron skillet or griddle pan over medium-high heat. In a large bowl, combine the meat mixture, breadcrumbs, parsley, pecorino-romano, egg, garlic, onion, milk and sage; season with nutmeg, salt and lots of pepper. Form the mixture into 4 patties (thinner at the center and thicker at the edges for even cooking).
Drizzle the burgers all over with a liberal amount of EVOO. Place in the hot skillet and cook, turning once, for 10 minutes. Top each burger with 2 slices of provolone and tent with foil to melt.
While the burgers are working, in a medium saucepan, heat the tomatoes. Stir in the basil and oregano; season with salt and pepper.
Place the burgers on the roll bottoms, then top with the sauce and roll tops.