Vegetarian Bourguignon

Name: Vegetarian Bourguignon
Ingredients: 1 pint brown champignon mushrooms; 2 tablespoons extra-virgin olive oil, divided; 1 yellow onion, sliced; 1 large carrot, cut into 1-inch chunks; 1 large clove garlic, peeled and slightly crushed; 2 sprigs fresh thyme, leaves only; 1 sprig fresh rosemary, leaves removed and chopped; 1 eggplant, cut into 1 1/2-inch cubes; 0.5 cup hearty red wine; 0.5 cup low-sodium vegetable broth; 2 Roma tomatoes, chopped; 2 tablespoons tomato paste; salt and ground black pepper to taste