Pulse carrot, celery, and red bell pepper in a food processor until minced. Set aside.
Heat olive oil and Earth Balance in a large pot over medium high heat. Put Beyond Burger patties into the pot and break apart into little bits using a wooden spoon. Stir occasionally until Beyond Burger is lightly browned.
Add minced carrots, celery, and red bell pepper. Cook until vegetables are softened.
Stir in tomato paste and vinegar. Cook tomato paste and vinegar for about 3 minutes.
Using your hands, crush the whole peeled tomatoes into the pot including all its juices/puree.
Mix in salt, black pepper, crushed red pepper flakes, thyme, basil, water, and nutritional yeast. Bring to a boil, then lower the heat. Simmer for 30 minutes, uncovered, occasionally giving it a stir.
While the sauce is simmering, cook pasta in a large pot of boiling salted water, stirring occasionally, until very al dente (about 1-2 minutes less than package instructions). Reserve 1 cup of pasta cooking liquid, then drain. Put pasta back into the same pot.
Ladle in bolognese sauce. Toss and coat pasta, or until pasta is perfectly coated with the sauce and perfectly al dente (the residual heat from the sauce will continue to cook the pasta). If the pasta sauce is too thick, add a little bit of pasta cooking liquid to loosen up the sauce.
Garnish with vegan parmesan (I love Violife brand) and fresh basil leaves.