Pasta Primavera

I've only had this dish once in a restaurant, so it's hard to compare, but I thought this recipe was absolutely amazing!

1/2 pound angel hair pasta or spaghetti
1 small bunch broccoli, about 1 heaping cup of florets
1 small zucchini, diced
4 asparagus spears
1/2 cup peas, fresh or frozen
1/2 cup snow peas
3 minced garlic cloves
3 Roma or other paste tomatoes, seeded and diced
12 basil leaves, chopped
4 Tbsp. butter
1/4 cup chicken broth (use vegetable broth for vegetarian option)
1/2 cup heavy cream
1/2 cup grated Parmesan cheese