Bring a large pot of water to a boil and season generously with salt.
kosher salt
Add the broccoli to the pot and cook for 30 seconds, then use a slotted spoon to remove and drain on a clean tea towel.
2 cups broccoli florets
Repeat with the asparagus and snap peas, but cook them for no more than 15-20 seconds.
½ lb asparagus, 1 cup snap peas
Add the pasta to the boiling water and cook until just shy of al dente according to the package instructions. Be sure to reserve some of the cooking water.
12 ounces short pasta
Heat the olive oil in a large skillet over medium heat. Add the sliced leeks with a pinch of salt and cook, stirring frequently, until soft and just starting to turn translucent, about 4 minutes.
3 tablespoons extra virgin olive oil, 1 leek
Add the garlic and cook for about 30 seconds or until fragrant, then pour in the white wine and let it simmer for about 1 minute to cook off the alcohol.
2 garlic cloves, ½ cup dry white wine
Add the broccoli, asparagus, and snap peas to the pan and toss to combine.
When the pasta is ready, transfer it to the pan along with the defrosted peas and about ½ cup of reserved pasta water.
1 cup frozen peas
Toss everything together over medium heat, then add the butter, lemon zest, and lemon juice. Toss vigorously until the butter melts and emulsifies with the pasta water.
3 tablespoons unsalted butter, 1 lemon
Add the grated Parmigiano Reggiano and half of the parsley, then continue tossing until the pasta becomes glossy and well coated. Add a splash of more pasta water if needed to loosen the sauce.
½ cup Parmigiano Reggiano, ¼ cup flat leaf parsley
Taste and adjust seasoning with salt, black pepper, and additional lemon juice if needed.
freshly cracked black pepper
Serve immediately with the remaining parsley and extra Parmigiano Reggiano on top.