Heat oil in a large skillet over medium-high heat. Add mushrooms and cook, stirring once, until browned, about 4 minutes. Add onion, two-thirds of the garlic and thyme; cook, stirring occasionally, until the onion is translucent, about 3 minutes. Add tomato paste, salt and 1/4 teaspoon pepper and cook, stirring, for 1 minute. Stir in wine and tomatoes and bring to a simmer. Cover and cook for 5 minutes.