How to Make It
Preheat the oven to 425°. In a bowl, toss the Broccolini and garlic with 1/4 cup of the olive oil and season with sea salt and pepper; spread on a rimmed baking sheet. In another bowl, toss the tomatoes with the remaining 2 tablespoons of olive oil, 1/2 tablespoon of sea salt and 1 teaspoon of pepper and spread on a rimmed baking sheet. Roast the vegetables for about 25 minutes, until the Broccolini is tender and charred in spots and the tomatoes are very juicy but not broken down.
Meanwhile, in a large pot of salted boiling water, cook the scallions until just softened, 1 minute. Using a slotted spoon, transfer the scallions to a bowl. Add the asparagus to the pot and cook until just crisp-tender, about 2 minutes. Using a slotted spoon, transfer the asparagus to the bowl.
Add the pasta to the boiling water and cook until just al dente. Drain, reserving 1/2 cup of the pasta cooking water.
Return the pasta to the pot. Add the roasted Broccolini, scallions, asparagus, butter, crushed red pepper and half of the parsley. Add the reserved pasta water and cook until the pasta is al dente. Gently fold in the roasted tomatoes and any juices and season with sea salt and pepper. Garnish with the shaved cheese and the remaining parsley and serve right away.