Cook pasta as directed on package; drain, reserving the liquid. Set pasta aside; pour liquid back into the pot and bring to a boil.
Cut broccoli into bite-sized florets, cut carrots into 1/2 inch rounds, and slice bell pepper. Add vegetables to water and boil for 2 minutes, then remove from heat and set aside.
Heat a large skillet over medium and add oil. Dice onion and mince garlic; add both to hot oil and sauté 4-5 minutes until onion becomes soft.
Cut zucchini and yellow squash in half lengthwise and then into half-moons. Add to onion and garlic. Cook for 2-3 minutes more, stirring occasionally.
Add remaining vegetables, broth, 1 teaspoon zest of the lemon, and the juice of the lemon. Bring to a boil, then reduce heat and simmer for 3-4 minutes.
Add cooked pasta, grated cheese, and chopped parsley. Toss to combine and serve with grapes on the side.