Bring a large pot of salted water to boil while you prep the vegetables.
Start cooking the pasta when you start cooking the vegetables.
In a large skillet, heat the 1/4 cup of olive oil over medium heat and cook the garlic for a few minutes. Add any firm vegetables and the stalks of things to the garlic, then add 1/4 cup of the pasta water. (You don't need to measure - just use a ladle to scoop some out.) Partially cover so some of the steam can escape and cook until crisp tender, about 4 minutes.
Take the lid off and any quick-cooking vegetables, like broccoli and asparagus tips and cook a 2-3 minutes.
Add 1 cup of pasta water, the green onions and peas and drizzle the remaining tablespoon of olive oil. Bring to a rapid boil and cook until the water is reduced by half.
Stir in the ham.
When the pasta is done, add it to the skillet. You can just lift it out with tongs and put it straight into the sauce.
Add the cream and stir until the sauce is coating the pasta. If it seems too dense, add more pasta water and/or cream.
Turn the heat off and stir in the Parmesan cheese.