1. Bring 4 quarts water to boil in large pot. Pat chicken dry with paper towels and season with salt and pepper. Melt 1 tablespoon butter in large nonstick skillet over medium heat. Cook half of chicken until golden, 1 to 2 minutes per side. Transfer to bowl. Repeat with additional 1 tablespoon butter and remaining chicken.

2. Add additional 1 tablespoon butter and asparagus to empty skillet and cook until asparagus is just tender, about 5 minutes. Add garlic and cook until fragrant, about 30 seconds. Transfer to bowl with chicken and cover to keep warm.

3. Add 1 tablespoon salt and pasta to boiling water and cook until al dente. Reserve 1/2 cup cooking water. Drain pasta and return to pot. Add remaining butter, chicken, asparagus, lemon juice, cheese, and parsley to pot and toss to combine, adding reserved pasta water as needed. Season with salt and pepper. Serve.