Bring a large pot of salted water to a boil.
Cook pasta according to package directions, adding the asparagus and peas during the last 3 minutes of cooking time.
Reserve 1/2 cup of pasta cooking water, then drain the pasta and vegetables.
In the same pot, heat olive oil over medium heat and sauté minced garlic for 1 minute until fragrant.
Whisk in heavy cream and bring to a light simmer.
Return the pasta and vegetables to the pot and toss to coat.
Stir in Parmesan cheese, lemon zest, and lemon juice, adding reserved pasta water as needed for consistency.
Season with salt and black pepper to taste.
Garnish with fresh mint and serve immediately.