Warm olive oil in a large skillet over medium heat. Add the chopped onion, minced garlic, diced carrots, and celery, and stir to combine. Cook for 5-7 minutes, or until the vegetables are tender and aromatic.
Stir in the lentils, crushed tomatoes, tomato paste, and vegetable broth. If using, add the balsamic vinegar at this stage.
Add the oregano, basil, bay leaves, salt, and pepper, and stir to combine. Stir everything together, then reduce to a gentle simmer. Cover the pan and cook for 25-30 minutes, stirring occasionally, until the lentils are soft and the sauce has thickened.
Once the lentils are cooked, taste the sauce and adjust the seasoning with more salt or pepper if needed. Remove the bay leaves before serving.
Serve the lentil bolognese atop your preferred pasta, like spaghetti or penne. Top with fresh parsley and a dusting of vegan parmesan, if you like.