Step 1Cook the pasta in boiling salted water until al dente, 12 minutes.
Step 2Meanwhile, cut the guanciale into strips about 2 inches long and one-fourth-inch thick.
Step 3Heat 1 tablespoon of the oil in a large skillet over medium-high heat. Add the garlic and cook until fragrant, 1 minute. Add the guanciale and cook until lightly brown, another minute (it will not cook like bacon). Add the onion and cook another minute. If necessary, spoon excess fat from the pan. Add the tomatoes and cook 2 minutes. Add salt to taste and the red pepper flakes. Discard the garlic.
Step 4Drain the pasta and add to the skillet. Add the Parmigiano-Reggiano and pecorino Romano. Add the remaining tablespoon of oil and toss together.