Cook the vegetables: Heat 2 Tablespoons butter in a large pan over medium heat. Add the shallots and cook, tossing, for 2-3 minutes, until soft. Add a large drizzle of olive oil, the mushrooms, tomatoes, and thyme to the pan. Cook for another 5-6 minutes, until very soft and cooked down. Add the garlic and cook for 30 seconds, until fragrant. Season with salt and pepper.