Preheat oven to 400°F.
Cook the pasta in plenty of salted water until just al dente, drain, and set aside.
As the pasta cooks, prepare the vegetables: Cut the broccoli into small florets, slice the bell pepper into strips, and halve the cherry tomatoes. Grate the garlic clove. Chop the basil leaves.
Blanch the broccoli in boiling salted water for 2–3 minutes, then drain.
In a bowl, combine heavy cream, vegetable broth, basil, and grated garlic. Season with salt and pepper.
Set the pasta, broccoli, bell pepper, tomatoes, and peas in a large casserole dish. Pour the cream evenly over the mixture over and mix well.
Sprinkle generously with mozzarella and bake for about 20 minutes, until the cheese is golden brown and the casserole is bubbly.
