1. Prepare the ingredients by trimming and cutting asparagus into 2-inch pieces, seasoning the chicken breasts with salt and pepper, grating the zest and extracting juice from a fresh lemon, and mincing fresh garlic. Cook bowtie pasta in salted boiling water, adding asparagus during the last 2 minutes of cooking. Drain and set aside.
2. Heat olive oil or butter in a skillet over medium heat. Cook the seasoned chicken breasts for 6-7 minutes on each side until their internal temperature reaches 165°F. Remove from the skillet and let them rest before slicing into bite-sized pieces.
3. Using the same skillet, melt butter over medium heat. Add minced garlic and sauté for about 30 seconds until fragrant.
4. Pour in heavy cream or half and half, letting it simmer for 2-3 minutes while stirring continuously.
5. Reduce the heat and stir in Parmesan cheese, lemon zest, and lemon juice to form a smooth sauce. Adjust seasoning with salt and black pepper to taste.
6. Add the cooked pasta and asparagus into the skillet. Toss them in the creamy sauce until well combined.
7. Incorporate the sliced chicken into the pasta mixture, gently mixing it all together.
8. Allow the dish to cook for an additional 2 minutes over low heat to meld the flavors.
9. Serve the pasta on a platter, optionally garnishing with fresh parsley, lemon slices, and additional Parmesan cheese for extra flavor.
10. Pair the dish with a green salad or garlic bread for a complete meal, and store any leftovers in an airtight container for reheating later.