12 ounces short pasta, such as penne or fusilli
4 garlic cloves, thinly sliced
2 1/2 teaspoons (or more) kosher salt
3/4 teaspoon (or more) freshly ground black pepper
1 (10-ounce) bag frozen broccoli florets
6 ounces green beans, preferably haricots verts, trimmed
8 ounces large shrimp, peeled, deveined, tails left on
1 pint cherry tomatoes, sliced in half
1 cup frozen green peas
3 tablespoons unsalted butter
1 teaspoon finely grated lemon zest
3/4 cup finely grated Parmesan, plus more for serving
1/4 cup coarsely chopped basil
Red pepper flakes (for serving; optional)
Place pasta in a large, wide-bottomed pot or large, wide, straight-sided pan. Add garlic, salt, black pepper, and 3 1/2 cups hot water. Cover and bring to a boil. Once boiling, uncover and cook, setting a timer for cooking pasta according to package directions and stirring often. When 5 minutes remain on timer, stir in broccoli and green beans. Cover pot and return to a boil. (If pot starts to dry out at any point, add another 1/2 cup water.) When 2 minutes remain on timer, stir in shrimp, tomatoes, peas, and butter. Cover and continue to cook 2 minutes, then uncover and cook, stirring, until pasta is tender, shrimp are cooked through, and water is almost completely evaporated, about 1 minute more.
Remove from heat. Stir in lemon zest and 3/4 cup Parmesan and toss to coat. Season with more salt and pepper, if needed.
Divide pasta among plates. Top with basil, additional Parmesan, and red pepper, if using.