Preheat oven to 425 degrees. Line a 13 x 9 baking dish with foil. Combine tomatoes garlic, anchovies, butter, and red pepper flakes. Season with salt and black pepper. Use your hands to mash all ingredients together and break up tomatoes.
Roast, stirring halfway through, until garlic is very soft and mixture thickens and caramelizes, about 30 minutes. Using a potato masher, mash to break up garlic and tomatoes.
Meanwhile, cook pasta in a large pot of boiling salted water, stirring occasionally, until al dente. Drain, reserving 1/2 cup pasta cooking liquid.
Return pasta to pot and add tomato sauce and pasta cooking liquid. Cook over medium-high heat, tossing until sauce coats pasta, about 3 minutes.
Serve topped with Parmesan and more red pepper flakes.
(Can also be used as a pizza sauce, for dipping or blend with stock for tomato soup.)