In a food processor, pulse the whole tomatoes until coarsely ground and no large pieces remain. You could use flavored crushed tomatoes and skip this step.
Heat oil in a 10-inch, non-stick skillet (All-Clad makes the best 10-inch, non-stick skillet in the world).
When skillet is hot, add onion and 1/4 teaspoon salt and cook until softened - about 5 minutes.
Stir in garlic and pepper flakes and cook until you can smell them - about 30 seconds.
Brown meat, breaking up the meat, until lightly browned and no longer pink - about 5 minutes.
Take the 2" portions of the UNCOOKED broken pasta and scatter over the meat, then pour processed tomatoes over pasta.
Cover, increase heat to medium-high, allow to cook, stirring often, or until pasta is tender - about 20 minutes
Off heat - scatter mozzarella onto the mixture and half the Parmesan.
Season with salt and pepper to taste.
Dollop heaping tablespoons of ricotta over noodles, then sprinkle with remaining mozzarella and Parmesan.
Cover and let stand off heat until cheese melts.