Cook pasta according to package directions in a Dutch oven; drain. Return pasta to pan. Set aside.
Trim asparagus. Remove tips; set tips aside. Bias-slice remaining asparagus stalks into 1-1/2-inch pieces. Set stalks aside.
In a wok or 12-inch nonstick skillet stir-fry garlic and red pepper in hot oil for 15 seconds over medium-high heat. Add carrots and leek; stir-fry for 2 minutes. Add tomatoes; stir-fry for 1 minute more. Add asparagus stalks, vermouth, and salt. Cook, uncovered, for 2 to 3 minutes or until asparagus is crisp-tender. Add asparagus tips. Cook, uncovered, for 1 minute more. Add butter, stirring till melted. Add asparagus mixture and basil to pasta; toss gently to coat. Transfer to a warm serving dish. Garnish with nuts and shaved cheese. Makes 4 main-dish servings.