Bring a large pot of lightly salted water to boiling; add pasta and cook according to package directions. Drain and rinse pasta under cold water; drain again. Transfer pasta to a large bowl.
Heat 1 tablespoon of the oil in a large nonstick skillet over medium-high heat. Add the garlic; cook 30 seconds until fragrant. Add zucchini; cook and stir for 1 minute. Add snap peas; cook 30 seconds. Stir in tomatoes; cook 30 seconds or until beginning to soften. Transfer vegetable mixture to pasta bowl; toss well.
For shallot-mustard dressing, in a small bowl combine shallot, vinegar, mustard, salt, and pepper. Slowly whisk in remaining oil; stir in parsley. Pour dressing over pasta mixture; toss well.
Serve immediately or cover and refrigerate for 4 hours or up to 3 days to allow flavors to meld. Before serving, sprinkle each serving with Asiago cheese.