Bring a large pot of water to a boil. Add salt and pasta to boiling water. Cook for 11 minutes, stirring occasionally. Drain well. Pour the pasta back into the pot.
Meanwhile, in a large skillet, heat the olive oil over medium high heat. Add the asparagus, peppers, and broccoli. Sauté for 2 to 3 minutes, stirring occasionally. Add in the zucchini and cook for 1 to 2 minutes or until vegetables are tender, but still crisp. Season vegetables with salt and pepper, to taste. Transfer the vegetables to a large plate or bowl.
Place the skillet back on the stove. Melt the butter over medium heat. Add the shallot and garlic and cook for 2 minutes. Stir in the lemon zest and vegetable broth. Simmer until the broth reduces by half, about 4 to 5 minutes. Stir in the heavy cream and 2 tablespoons of lemon juice.
Stir the peas into the pot with the pasta. Stir in the cooked vegetables. Pour the lemon cream sauce over the pasta and vegetables and stir until well combined. Stir in the Parmesan cheese and remaining tablespoon of fresh lemon juice. Gently stir in the tomatoes and basil. Season with salt and black pepper, to taste.
Pour the pasta primavera into a large serving bowl or dish. Garnish with parsley, extra Parmesan cheese, and crushed red pepper flakes. Serve warm.