Season the chicken:
Sprinkle the chicken cutlets with ¼ teaspoon of pepper and 1/8 teaspoon of salt on both sides.
Cook the chicken:
Heat the olive oil in a large skillet over medium heat. Add the chicken cutlets and cook, turning once, until browned and an instant-read thermometer inserted into the thickest part registers 165°F, about 6 minutes in total. Once done, transfer the chicken to a plate.
Make the sauce:
In the same skillet, add the sliced shallot and minced garlic. Cook, stirring constantly, for about 1 minute until the shallots begin to soften.
Increase the heat to medium-high and add the chicken broth. Cook for about 2 minutes, until the broth is reduced by half.
Add cream and lemon juice:
Reduce the heat back to medium, and stir in the heavy cream, lemon juice, and any accumulated juices from the chicken. Add the remaining ¼ teaspoon of pepper and 1/8 teaspoon of salt. Let the sauce simmer for about 2 minutes, allowing it to thicken.
Finish the dish:
Return the cooked chicken to the skillet, turning it to coat with the creamy sauce. Let it simmer for another 2 minutes to ensure the chicken is well-coated and heated through.
Serve and garnish:
Sprinkle the chicken with fresh parsley and serve with lemon wedges on the side for an extra burst of citrusy flavor.