Heat a large nonstick skillet over medium-high heat. Add oil to pan; swirl to coat. Add asparagus; sauté 3 1/2 minutes. Add garlic; sauté for 1 minute. Add tomatoes; cook for 6 minutes or until tomatoes are tender.
Combine cheese, salt, pepper, and egg in a large bowl, stirring with a whisk.
Add pasta to boiling water; cook 10 minutes or until al dente. Drain and toss pasta immediately with egg mixture. Add tomato mixture, tossing until sauce thickens. Divide pasta equally among 4 bowls. Sprinkle each serving with 1 tablespoon basil. Serve immediately.