If the chicken breasts are thick, slice them horizontally or pound them to an even thickness of about 1/2 inch. Season with the divided salt and pepper, lightly dredge each piece in flour, and shake off the excess.

Heat the olive oil and 1 tablespoon of butter in a large skillet over medium-high heat. Cook the chicken for approximately 4 to 5 minutes per side, until browned and nearly cooked through, then transfer it to a plate.

Add the asparagus to the skillet and cook for 3 to 4 minutes, stirring occasionally, until bright green and just tender. Transfer the asparagus to the plate with the chicken.

Reduce the heat to medium and add the remaining tablespoon of butter. Sauté the minced garlic for about 30 seconds, stirring constantly and taking care not to let it brown.

Pour the chicken broth into the skillet and scrape up the browned bits from the bottom. Simmer for 2 to 3 minutes so the broth picks up the savory flavor from the pan.

Stir in the heavy cream, Parmesan, lemon zest, and lemon juice. Simmer gently for 2 to 4 minutes, until the sauce thickens slightly, keeping the heat low enough that the cream does not boil vigorously.

Return the chicken and asparagus to the skillet and spoon the sauce over the chicken. Simmer for 2 to 3 minutes, until the chicken reaches 165°F in the thickest part and the asparagus is tender.

Finish with chopped parsley and, if desired, a little additional lemon zest or Parmesan. Serve immediately while the sauce is warm and creamy.