Heat wok or large, deep skillet over medium-high heat. Add butter, onion and garlic and saute until onion is softened, about 2 minutes. Mix in asparagus, mushrooms, cauliflower, zucchini and carrot and stir-fry 2 minutes. (At this point, remove several pieces of asparagus tips, mushrooms and zucchini and reserve for garnish.)
Increase heat to high. Add cream, stock and basil and allow mixture to boil until liquid is slightly reduced, about 3 minutes. Stir in peas, ham and green onion and cook 1 minute more. Season to taste with salt and pepper.
Add pasta and cheese, tossing until thoroughly combined and pasta is heated through. Turn onto large serving platter and garnish with any reserved vegetables. Serve immediately.