Get a large pot of water boiling, then add enough salt to make it taste salty. Boil the asparagus spears for about 1 to 2 minutes, then remove and slice into bite-sized pieces. Boil the broccoli florets for about 3 minutes, remove and spread on a baking sheet to cool. If you are using green beans, boil them for about 2 to 3 minutes, then add them to the baking sheet. If you are using frozen peas, set them out to thaw. If fresh, boil them for 1 minute, then move to the baking sheet.
When this is done, dump the water from the pot and refill it to boil the pasta. You'll need to add more salt, too. You don't want to use the vegetable water for the pasta because it'll give it an off taste. Cook the pasta until it's almost done -- just a shade too much al dente to enjoy, but still mostly cooked.
Meanwhile, get a large saute pan hot and add the olive oil and sliced mushrooms. Toss to combine and sear the mushrooms over high heat. Sprinkle salt over them now. You want them to release their water. When that water has mostly boiled away, move to the next step.
Add the butter, red pepper flakes, garlic and tomatoes and toss to combine. Cook this with the mushrooms for 2 minutes, then add all the vegetables and toss to combine. Pour in the chicken broth and get this boiling.
To finish, add the herbs, pasta, grated cheese and half the cream. Toss to combine well, and add the rest of the cream if the sauce looks dry. Grate lots of black pepper over everything and serve.