Boil a large, salted pot of water for the pasta. Cook pasta according to package directions.
Preheat grill to high heat.
Meanwhile, prepare your veggies. Slice the zucchini in half, and then slice each half lengthwise. Cut the yellow pepper in half and remove the seeds. Husk the corn. Coat the veggies with a light layer of olive oil, and then sprinkle them lightly with garlic powder and salt & pepper.
Reduce grill to medium-high heat. Grill the corn for 10-12 minutes total (rotate it a few times) and the zucchini, peppers, and asparagus for three minutes each per side.
Once the pasta is cooked, drain it and then rinse it under cool water. Add to a large bowl. Toss it with three tablespoons of olive oil, the lemon juice and zest, and the garlic.
Once the veggies have cooled somewhat, use a knife to cut the kernels of corn off the cobs, and then slice the other veggies into bite-size pieces. Add them to the bowl. Tear the basil and add it to the bowl, and shave the parmesan add and it as well. Toss the salad. Can be served right away or refrigerated first. Will keep in the fridge for a few days.