Add stock, linguine, onion, broccoli, asparagus, mushrooms, garlic, red pepper flakes, salt and pepper to a large pot set over high heat. Drizzle the olive oil over the top.
As soon as it comes to a boil, set the timer for 7 minutes and start tossing constantly with long-handled tongs.
Continue boiling and tossing. As soon as the 7 minutes is up, add the peas, parsley, heavy whipping cream, parmesan, and lemon zest and continue cooking, tossing constantly, for 1-2 more minutes, until the pasta and veggies appear tender.
Remove from heat. Let the pasta sit for a couple of minutes to cool; the sauce will continue to thicken during that time.
Taste and add additional salt and pepper if desired. Garnish with additional Parmesan cheese.