Bring a large pot of salted water to a boil over medium high heat. Add the pasta and cook, stirring frequently about 7 minutes; add asparagus. Once both are tender add peas and spinach and simmer until spinach is wilted, about 30 seconds. Reserve about 1/2 cup of the pasta water, then drain pasta and veggies.
In the meantime, heat a skillet over medium high heat and cook the garlic, stirring, until it start turn golden. Add the tomatoes and cook down until reduced to a pasta sauce, about 5 minutes. Add cream and cook about 3 minutes more (sauce should be thick enough to coat pasta).
Return pasta and veggies to large pot and add the creamy tomato sauce, Parmesan cheese and chili flakes; toss to coat.
After draining the pasta and vegetables, return them to the pot and add the creamy tomato sauce, the reserved pasta cooking liquid if necessary, the Parmigiano, and chili flakes; toss to coat. If necessary, thin sauce with reserved pasta cooking water. Serve with grated Parmesan cheese.