Heat 2 tbsp olive oil in a large pot over medium-high heat. Add mushrooms and cook until browned, about 10 minutes. Remove and set aside.

In the same pot, heat remaining oil. Add onion, carrots, and celery. Cook until softened, about 5 minutes.

Add garlic and tomato paste. Cook for 1 minute.

Pour in red wine, scraping up any browned bits from the bottom of the pot.

Add vegetable broth, bay leaves, and thyme. Bring to a boil, then reduce heat and simmer for 15 minutes.

Return mushrooms to the pot and simmer for another 15 minutes.

Stir in cornstarch mixture and cook until sauce thickens, about 2 minutes.

Remove bay leaves and thyme sprigs. Season with salt and pepper.

Serve over pasta or mashed potatoes, garnished with fresh parsley.