In Dutch oven or large saucepan, cook linguine to desired doneness as directed on package.
Meanwhile, heat oil in large nonstick skillet over medium-high heat until hot. Add garlic; cook about 30 seconds, stirring constantly. Reduce heat to medium; add sugar snap peas and asparagus. Cover; cook 3 minutes. (If vegetables begin to stick, add 1 to 2 tablespoons water to skillet.)
Add tomatoes; cook an additional 2 to 4 minutes or until vegetables are crisp-tender, stirring occasionally. Stir in basil, salt and pepper.
Drain linguine; return to Dutch oven. Add vegetable mixture; toss to mix. Sprinkle with cheese.