Step 1

Toss tomatoes, 1 tablespoon oil, minced garlic, 1/4 teaspoon salt, and 1/4 teaspoon pepper together in bowl; set aside.

Step 2

Bring 4 quarts water to boil in large Dutch oven. Add pasta and 1 tablespoon salt and cook, stirring often, until al dente. Drain pasta and return it to pot.

Step 3

Meanwhile, heat 3 tablespoons oil in 12-inch nonstick skillet over medium-low heat until shimmering. Add zucchini, pepper flakes, sliced garlic, and 1/2 teaspoon salt and cook, covered, until zucchini softens and breaks down, 10 to 15 minutes, stirring occasionally. Add asparagus, peas, and 3/4 cup water and bring to simmer over medium-high heat. Cover and cook until asparagus is crisp-tender, about 2 minutes.

Step 4

Add vegetable mixture, chives, lemon juice, and remaining 2 tablespoons oil to pasta and toss to combine. Transfer to serving bowl, sprinkle with Pecorino, and drizzle with extra oil. Spoon tomatoes and their juices over top and sprinkle with mint. Serve, passing extra Pecorino separately.