Heat the olive oil in a large skillet or pot over medium-low heat. Add the onions and cook until starting to turn translucent, a couple of minutes. Add the garlic and stir, cooking 1 minute, making sure not to brown the garlic.
Add the ground beef and cook until brown. Drain off most of the excess fat. Add the ground thyme, red pepper flakes and some salt and pepper. Stir to combine. Dump in the canned tomatoes with their juices. Stir, reduce the heat to low and cover the pot. Cook for 30 minutes, stirring a couple of times. Uncover the pot and cook an additional 30 minutes.
Cook the rigatoni according to the package directions--don't overcook! Drain and place individual portions into bowls.
Stir 1/4 to 1/2 cup grated Parmesan into the sauce. Check and adjust the seasonings. Ladle the sauce over the cooked pasta, top with more Parmesan and serve with extra Parmesan for sprinkling.
If cooking ahead of time to reheat later, oil the cooked pasta before refrigerating. Refrigerate the sauce separately. To reheat, put the pasta in microwave-safe bowls, add some sauce and microwave. Sprinkle with cheese and serve.