Preheat broiler to low. Line a baking sheet with parchment paper.
In a large bowl, toss together olive oil, portobello mushrooms, garlic, yellow onion, celery and carrots.
Spread mixture on baking sheet and broil until vegetables are charred in spots, flipping once, about 20 minutes. Let cool for 5 minutes.
Squeeze roasted garlic out of skins; discard skins. Transfer garlic and vegetable mixture to a food processor. Pulse until finely chopped; set aside.
In a large skillet, heat olive oil over medium-high heat. Add cremini mushrooms and cook until bottoms are browned, about 3 minutes. Stir and continue to cook until mushrooms are browned on all sides, about 5 minutes.
Add tomato paste and oregano and cook, stirring constantly, about 1 minute. Add red wine and cook until thickened, another additional minute.
Stir in roasted vegetable mixture and season with salt and black pepper. Remove from heat.
Bring a large pot of salted water to a boil. Add pasta and cook until a few minutes before al dente. Drain water, reserving 1½ cups of cooking liquid.
Transfer cooked pasta to skillet and heat over medium. Add Parmesan cheese and olive oil. Stir in reserved cooking liquid, gradually, until sauce is creamy. Season with salt.
Divide pasta and sauce among 4 bowls, garnished with additional Parmesan cheese.