Pour olive oil into a large, cold skillet. I used a 10" skillet, the biggest I have. Add garlic, onion, carrots, and spices. Heat over medium-high heat until onions and carrots are beginning to soften and garlic is fragrant.
Add green beans and peas, cook until crisp-tender.
Add zucchini, cook until tender. From start to finish, the oil, spices, and veggies probably cooked for a half hour or a little longer. Near the end, I put the lid on the sauté pan so that the veggies would steam and cook more quickly.
To serve, spoon warm pasta onto plates.
Top pasta with the oil and veggie sauce.
Sprinkle generously with grated cheese.