In a large pot cook pasta according to package directions. Drain; reserve 1/2 cup pasta water. Return pasta to pot. Add 1 Tbsp. of the peanut oil. Toss until well combined; set aside.
Heat a 14-inch flat-bottomed wok or 12-inch stainless-steel skillet over high heat until a bead of water vaporizes within 2 seconds of contact. Swirl in remaining 1 Tbsp. peanut oil.
Add asparagus; stir-fry 2 minutes or until bright green. Add garlic; stir-fry 10 seconds or until fragrant. Add cherry tomatoes and 1/2 tsp. of the salt; stir-fry 30 seconds. Add basil and olives; stir-fry 30 seconds. Remove pan from heat. Add pepper, remaining 1/4 tsp. salt, and pasta; toss to combine. Add enough reserved pasta water to create desired consistency. To serve, sprinkle with Parmesan cheese. Pass with lemon wedges, if desired.