Strain liquid from tomatoes and reserve for another use (works great for Bloody Marys or adding to tomato or minestrone soup).
Divide the tomatoes between 2 sheet trays and spread into an even layer. Add 3 smashed garlic cloves, 2 sprigs oregano, 2 sprigs rosemary and 1 Pecorino rind to each tray. Drizzle half the olive oil over each tray. Sprinkle half the red pepper flakes over each tray and season with salt and pepper. Roast, rotating sheet trays halfway through, until the tomatoes are just beginning to char on the bottom, about 25 minutes.
Add the tomatoes to a large saucepan and crush with a potato masher until you reach desired consistency. Bring to a simmer and season with salt and pepper, and drizzle with more olive oil.
Cook the pasta 2 minutes less than indicated on the box instructions. Transfer cooked pasta to sauce in saucepan, toss and cook for an additional 2 minutes. Finish with butter and grated Pecorino.