Prep the chicken. Pat the chicken dry with paper towels. Season both sides with salt and pepper. If the breasts are thick, pound them to an even thickness for quicker, more even cooking.
Heat the pan. Set a large skillet (12 inches or wider) over medium-high heat.
Add 1 tablespoon olive oil. When the oil shimmers, add the chicken in a single layer.
Sear the chicken. Cook without moving it for 3–4 minutes, until deeply golden on the first side. Flip and cook another 3–4 minutes.
The chicken doesn’t need to be fully cooked yet; you’ll finish it in the sauce. Transfer to a plate.
Sauté the aromatics. Reduce heat to medium. Add another tablespoon of olive oil if the pan looks dry.
Stir in the minced garlic and thyme. Cook 30–45 seconds until fragrant, scraping up browned bits with a wooden spoon.
Build the sauce base. Pour in the chicken broth. Add the zest of the lemon and the juice of half the lemon.
Simmer for 1–2 minutes to slightly reduce. Stir in the butter until the sauce looks glossy. For a brinier kick, add capers now.
Add the asparagus. Place the asparagus in the sauce in a single layer if possible.
Sprinkle with a pinch of salt and red pepper flakes if using. Cook 3–4 minutes, turning once, until bright green and crisp-tender.
Return the chicken. Nestle the chicken back into the pan, along with any juices on the plate. Spoon sauce over the chicken.
Simmer 2–4 minutes, or until the chicken reaches 165°F in the thickest part.
Finish with herbs and lemon. Turn off the heat. Stir in chopped parsley and taste the sauce. Add more lemon juice, salt, or pepper as needed.
If you like, sprinkle with Parmesan for a savory finish.
Serve. Plate the chicken with asparagus and spoon extra sauce over the top. Serve with rice, orzo, mashed potatoes, or crusty bread to soak up every drop.