Wash and trim the asparagus ends, about 1" from the bottom, and discard the ends. Cut them into 2-3 pieces and set aside.
Butterfly the chicken breasts on a cutting board by slicing them horizontally through the middle. Pat dry with a paper towel and season with salt and pepper on both sides.
Cook the pasta:
Bring a large pot of water to a boil and cook penne pasta according to package directions. During the last 5 minutes of cooking, add the asparagus to the pasta. Cook them with the pasta for about 5 minutes. Once the pasta is ready, reserve ½ cup pasta water, drain, and set aside.
Cook the chicken:
Heat a large pan over medium-high heat. Once hot, add the oil and heat it up. Place the chicken breasts in the hot pan and cook, without moving them, for 4 minutes on the first side, then once golden and seared, flip them over and continue cooking for an additional 4 to 5 minutes until the chicken breasts’ internal temperature reaches 165F. Remove them from the pan onto a cutting board.
Make the sauce:
To the same pan, add the butter and melt it, add the garlic, and stir to cook the garlic for about 30 seconds.
Add the chicken broth and milk or half and half to the pan, bringing it to a simmer while stirring the tidbits from the bottom of the pan. Add the thyme, stir to combine, reduce the heat to medium-low and simmer the sauce for 10 minutes.
Bring it together:
Once the sauce is ready, cut the chicken breasts diagonally into ½-inch strips and transfer them into the pan with the juices from the board.
To the sauce, add the cooked pasta and asparagus, parmesan cheese, and squeeze ½ of the lemon into the pan. Give everything a good toss to combine, and add half of the reserved pasta water to thin out the sauce. Add the rest if you want more sauce.
Serve with additional parmesan cheese over the top and a lemon wedge or extra squeese of lemon if desired.