Bring a pot of water to a boil. Cook the tortellini in the boiling water for a couple of minutes less than the package directions call for. Drain and set aside.
Melt the butter in a large skillet over medium-high heat. Add the garlic and onions and stir and cook for 1 minute. Add the cauliflower, carrots and asparagus and stir and cook 1 minute. Splash in the broth, then cook until the liquid reduces a bit, 2 to 3 minutes. Stir in the Parmesan and cream and cook until hot. Stir in the peas, ham and some salt and pepper and continue cooking to allow the peas and ham to heat up in the sauce. Add the basil and heat; stir in the tortellini. Check for seasoning, adding more if needed, and serve with extra Parmesan and basil.