Bring a large pot of water to a boil, salt it, add the pasta and cook until al dente. Drain, reserving 1/2 cup of the pasta cooking water.
While the pasta is working, In a deep skillet with a tight-fitting lid, heat the EVOO, 4 turns of the pan, over medium heat. Add the bacon and cook until crisp, 3 to 4 minutes. Add the onion and bay leaf, partially cover and cook until softened, about 10 minutes. Stir in the tomatoes, garlic, thyme and lots of pepper. Cover and cook over medium-high heat, shaking the pan occasionally, until the tomatoes burst, about 10 minutes. Remove the lid and mash up the tomatoes a bit with a potato masher. Stir in the parsley; discard the bay leaf.
Toss the pasta with the sauce and mixed cheeses. Add the pasta water as necessary to combine. Serve in shallow bowls.