Heat the olive oil in a large Dutch oven or deep skillet over medium-high heat.
Add the chestnut mushrooms and cook for 6–8 minutes until browned. Remove and set aside.
In the same pot, sauté the onion and carrots for about 5 minutes until softened.
Add the garlic and tomato paste, cooking for 1 minute while stirring continuously.
Pour in the red wine (or vegetable broth) and scrape the bottom of the pot to release any browned bits.
Stir in the vegetable broth, thyme, bay leaf, salt, and black pepper.
Return the mushrooms to the pot and bring the mixture to a gentle simmer.
Cover and cook for 25–30 minutes, allowing the flavors to develop and the sauce to thicken.
Remove the bay leaf and adjust seasoning to taste.
Garnish with fresh parsley and serve hot over mashed potatoes, rice, pasta, or with crusty bread.