Prepare pasta al dente according to package instructions. (I would add the pasta to the boiling water around the time you begin cooking the asparagus.)
Heat 2 Tbsp. oil in a large skillet over medium-high heat. (You will know that it is ready when the oil is shimmering, or it sizzles when you place a drop of water in the oil.) Season both sides of the chicken with a pinch of salt and freshly-cracked black pepper. Add the chicken to the skillet and cook for 3-4 minutes on each side, or until the chicken is fully cooked and the juices run clear. Remove chicken and set aside. Wait a few minutes, then slice the chicken into thin strips.
In the same skillet, add the remaining tablespoon of olive oil. Add asparagus, garlic, lemon juice and zest, and rosemary and saute for 4-5 minutes until the asparagus is cooked but still slightly crisp. Remove skillet from heat. Stir in Greek yogurt, Parmesan cheese, and baby spinach.
Once the pasta is finished cooking, drain the pasta but reserve 1/4 cup pasta water. Toss together the pasta, creamy vegetable mixture and the chicken. Add some of the reserved pasta water if needed to thin the sauce. Serve immediately, garnished with extra Parmesan and/or chopped fresh parsley.