Heat oil in a skillet (or pan) over medium heat. Add the onion and sauté until translucent, about 2 minutes.
Stir in the carrots, (celery if using), mushrooms, salt, and pepper. Sauté until mushrooms have cooked down and are turning golden, about 5-7 minutes.
Add tomato paste, spices and garlic. Roast for about 1-2 minutes longer.
Then add lentils, tomatoes and vegetable broth and stir to combine. Bring to a boil, then cover, reduce the heat to low, and simmer for about 15-20 minutes, until lentils are done and the bolognese sauce is thickened. Adjust consistency by adding more water if needed. Taste and adjust salt, pepper, and spices.
In the meantime, cook the spaghetti (or other pasta) in salted water until al dente, then drain.
Serve the lentil bolognese sauce over the spaghetti. Garnish with vegan parmesan cheese or yeast flakes and fresh herbs if you like.