In a large pot, bring salted water to a boil. Add the 10 ounces of pappardelle pasta and cook according to package instructions until al dente. Drain and set aside.
In a large skillet, heat 2 tablespoons of extra-virgin olive oil over medium heat. Add the diced onion and chopped carrot, sautéing until the onion is translucent, about 5 minutes.
Stir in the finely chopped cremini mushrooms and garlic. Cook for an additional 5-7 minutes, until the mushrooms are softened and the garlic is fragrant.
Sprinkle in the sea salt and freshly ground black pepper, stirring to combine. Add the balsamic vinegar and tamari, mixing well to incorporate.
Add the cooked green lentils and marinara sauce to the skillet. Stir to combine, letting the mixture simmer for about 10 minutes to meld the flavors.
Toss the cooked pappardelle pasta into the skillet, gently mixing to ensure the pasta is well-coated with the lentil and sauce mixture.
Divide the Lentil Pasta among serving plates. Drizzle with additional extra-virgin olive oil, sprinkle with Parmesan cheese or vegan Parmesan, and garnish with fresh parsley.