Heat a large pot of water to a boil for the pasta. Liberally salt the water, add pasta and cook to al dente. Reserve about 1/2 cup of the cooking water, a ladleful.
In a deep skillet, heat the EVOO over medium heat. Grate garlic into the pan and add crushed red pepper flakes and onion and cook for 5-6 minutes. Stir in the balsamic vinegar, then the tomatoes, then season with salt and pepper and simmer for 10 minutes over low heat.
Drain pasta and combine with pasta water, sauce and cheese and toss for 1 minute, then add arugula and toss to wilt, a minute more.