Step 1Set a large pot of salted water over high heat.
Step 2Meanwhile, heat the olive oil in a skillet over medium-high heat, add the pancetta and fry until crisp, 3 to 5 minutes. Remove the pancetta from the pan with a slotted spoon and set aside to drain on paper towels, leaving as much oil in the pan as possible.
Step 3Add the onion and cook until translucent, about 3 to 5 minutes. Add the garlic and cook until aromatic, 1 minute, being careful not to burn it. Add the minced mushrooms and cook until they release their moisture, stirring occasionally, 5 minutes.
Step 4Add the tomatoes and their juices, bring to a boil and simmer, stirring occasionally, until the flavors have melded, 10 to 15 minutes.
Step 5When the water is boiling, cook the rigatoni until al dente, 11 to 12 minutes. Drain the pasta and set aside.
Step 6Add salt and pepper to taste to the sauce, along with the parsley and thyme. Toss the pasta with the sauce and top with the pancetta and Parmesan to taste just before serving.