Put a large pot of water on to boil.
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.
Meanwhile, combine ricotta, herbs, the remaining garlic and 1/4 teaspoon pepper in a small bowl.
Cook pasta in the boiling water according to package directions. Using tongs or a slotted spoon, transfer the pasta directly to the skillet, allowing some of the pasta-cooking water to drip into the pan. Cook, stirring, until the pasta is coated with the sauce, about 1 minute. Serve the pasta topped with the ricotta mixture and more herbs, if desired.