Make a garlic-lemon butter. Mince and mash 2 cloves garlic and ½ teaspoon of the salt together to make a paste. Transfer to a small bowl, add 4 tablespoons of the butter and 1 tablespoon finely grated lemon zest, and mash together until combined; set aside.

Sauté the shallot in butter. Melt the remaining 2 tablespoons butter in a large Dutch oven or pot over medium-high heat. Add 1 medium minced shallot and sauté until softened and beginning to brown, 2 to 3 minutes.

Cook the pasta. Add 12 ounces dried short pasta, 4 cups hot water, and remaining 2 teaspoons salt. Cover and bring to a boil over high heat. Reduce the heat back to medium-high, uncover, and cook until the pasta is al dente, about 8 minutes. Stir the pasta occasionally, loosening noodles that stick to the bottom or sides of the pot.

Stir in the vegetables and cook until tender. Add the asparagus, zucchini, carrots, bell pepper, broccolini, sugar snap peas, and peas. Stir and cook uncovered until the vegetables are crisp-tender and the cooking liquid has reduced into a starchy sauce, about 2 minutes.

Finish with the tomatoes, cheese, and garlic-lemon butter. Stir in the tomatoes, ¾ cup grated Parmesan cheese, and garlic-lemon butter. Once the cheese and butter is melted, the cooking liquid should be significantly reduced, leaving only a silky, buttery sauce. Serve in bowls garnished with red pepper flakes, 2 tablespoons thinly sliced fresh basil leaves, and more Parmesan cheese.