Heat 1 tablespoon of olive oil in a large skillet or pot over medium heat.
Add the chopped chicken and sliced mushrooms to the skillet and cook, stirring occasionally, until the chicken is golden and cooked through and the mushrooms are softened, about 8–10 minutes.
Add the sliced garlic and halved tomatoes to the skillet and cook for 1 minute more, then transfer the chicken and vegetable mixture to a bowl and set aside.
Bring 4 cups of water to a boil in the same skillet or pot. Add the salt and the pasta and cook until al dente, about 9 minutes or according to package directions.
Drain off most of the cooking water, leaving about 1/2 cup in the skillet.
Return the reserved chicken and vegetable mixture to the skillet with the pasta. Add the chopped basil, black pepper, Parmesan, and the remaining 2 tablespoons olive oil, then toss everything together until well combined.
Adjust seasoning if needed and serve immediately.