Pat the chicken breasts dry and season both sides generously with salt and pepper. Pound to an even thickness of about ½ inch if needed.
Heat 2 tablespoons olive oil over medium-high heat in a skillet. Add the chicken breasts and cook 5-6 minutes per side until golden brown and cooked through (internal temperature 165°F/74°C). Remove chicken and set aside.
In the same skillet, sauté minced garlic for about 30 seconds until fragrant. Add asparagus and cook for 3-4 minutes until crisp-tender and bright green.
Reduce heat to medium-low. Pour in heavy cream, stirring to combine with garlic and asparagus. Add grated Parmesan, lemon juice, and lemon zest. Stir continuously until cheese melts and sauce thickens slightly, about 3-4 minutes. Season with salt and pepper to taste.
Return chicken breasts to skillet, spoon sauce over each piece. Warm together for 2-3 minutes to meld flavors.
Sprinkle chopped fresh parsley over the top. Serve immediately with your favorite sides.
