Penne with Tomato, Cream and Five Cheeses

heavy cream

chopped canned tomatoes in heavy puree

freshly grated pecorino romano cheese

freshly grated fontina cheese

crumbled gorgonzola cheese

ricotta cheese

thinly sliced mozzarella cheese

kosher salt, plus more for the pasta water

large, fresh basil leaves, coarsely chopped

pound penne rigate or conchiglie rigate

unsalted butter, thinly sliced