Cook the pasta according to the packet instructions until al dente but slightly firm. Do reserve some pasta water and set it aside. Remember to just toss the pasta in a teaspoon of oil in a colander.
Trim the woody edges of the asparagus and cut them into 1" length. Heat 1 teaspoon of butter and add the asparagus and broccoli to the pan and sauté them for 4 to 5 minutes until just done. Season with salt. Transfer the vegetables to the colander with pasta.
Heat the remaining butter+oil in a saucepan, add garlic and saute them for one minute. Whisk in the cream and simmer it.
When the cream begins to boil, add the peas and cook for a minute. Switch off the flame.
At this stage add the grated Parmesan cheese into the sauce, nutmeg, pepper, asparagus and cooked pasta. Toss them well and if you think the sauce is quite thick, add the reserved pasta water and stir to achieve the desired consistency. Serve Hot.