Add a pot to come to a boil.
Meanwhile, add the olive oil to a skillet with high sides set over medium heat. Once hot, add the shallots and garlic. Cook until softened, but not burned — about 3-5 minutes.
Add the broccoli, zucchini, and asparagus along with a pinch of salt and a bit of black pepper. Cook until softened (about 10 minutes).
In the meantime, once the water is boiling add a big pinch of salt and the pasta. Cook one minute shy of al dente (time it so that that's nearly done when the 10 minutes are up for the veggies).
Add the tomatoes and frozen peas to the veggies and stir. Once ready, add the pasta with a slotted spoon directly from the boiling water to the veggies along with the Locatelli, Parm, lemon juice, and a pinch of red pepper flakes. Add a little bit of pasta water if needed and stir. Bring to a low boil and cook until the sauce has thickened just a bit.
Finish in the pot or in a serving bowl by tearing the burrata balls and nestling them into the pasta. Finish with a touch of olive oil, salt, pepper, red pepper flakes, torn basil, and some freshly grated cheese.