Cook pasta in large pot of boiling salted water until al dente, tender but still firm, about 7 minutes. Drain, drizzle with olive oil to coat and set aside in large bowl.
Meanwhile, cook asparagus and beans in large pot of boiling water, uncovered, for 3 minutes or until bright green. Add peas and cook about 1 to 2 minutes more. Drain vegetables in a colander and set aside.
Heat 3 tbsp. olive oil in large skillet and sauté garlic over medium heat for 1 minute. Add drained vegetables and cook, stirring, about 2 minutes.
Add vegetable mixture to the reserved pasta. Toss until sauce coats pasta mixture. Mix in the cherry tomatoes and the Herbes de Provence. Season pasta with salt and pepper to taste.
Finish by topping with the Parmesan and a final drizzle of olive oil. Serve immediately.