Heat olive oil in a pot over medium heat. Add the onion and garlic, stir occasionally and sauté until light brown.
Add in carrots, red bell pepper, salt and pepper. Stir and let cook for about 5 minutes until the carrots soften. If needed, add few spoons of water.
Add in tomato paste and chopped walnuts, and cook for about 2 minutes.
Then add lentils, tomatoes, oregano, basil, and vegetable broth, and stir to combine. Bring to boil, cover the pan, and let simmer over low heat for about 30 minutes or until the lentils softens and the sauce thickens. Stir occasionally. Add more vegetable broth or water if needed. Taste and adjust salt and pepper. Finish with the white wine vinegar and sugar and stir to combine.
In the meantime, cook the pasta in salted water until al dente, then drain the pasta.
Serve the bolognese sauce over cooked pasta. Garnish with vegan cheese and chopped parsley.