In a large bowl, season the meat with plenty of salt and pepper. Form into 4 patties, thinner in the middle for more even cooking. Drizzle with EVOO.
In a saucepan, heat 2 tablespoons EVOO, 2 turns of the pan, over medium heat. Add the onion and cook until softened, about 5 minutes; add the garlic and cook for 2 minutes more, then stir in the tomatoes and season with salt and pepper. Lower the heat and simmer for 5 minutes; stir in the basil.
In large skillet, heat a drizzle of EVOO over medium-high heat. Add the patties and cook, turning once, until medium-rare, 7 to 8 minutes.
While the patties are cooking, in a small saucepan, melt the butter over medium heat; whisk in the flour for 1 minute, then whisk in the milk. Season with salt, pepper and the nutmeg, then cook until thickened, about 5 minutes. Stir in the ricotta and parmigiano-reggiano.
Spoon some red sauce on the roll bottoms, then top with the patties. Dollop the cheese sauce on the patties and set the roll tops in place.