Slice each chicken breast in half widthwise to make 4 thinner cutlets; pat dry and season both sides with coarse salt and freshly cracked pepper.
Whisk the all-purpose flour with a pinch of salt and some black pepper in a shallow bowl or pie tin for dredging.
Heat the olive oil in a large nonstick frying pan or rondeau over medium heat until shimmering, about 1½–2 minutes.
Dredge each chicken cutlet in the flour, shaking off excess, then add to the hot pan in a single layer (work in batches if needed).
Cook the chicken 3–4 minutes per side, until browned and almost cooked through; transfer to a plate and set aside.
Reduce heat to low, add the sliced garlic to the pan, and cook, stirring, for 1–2 minutes until fragrant but not browned.
Pour in the chicken stock and increase heat to high; boil until reduced by about half, about 4–5 minutes.
Stir in the lemon juice, butter, and season with additional salt and pepper as needed; keep over low heat and stir until the butter melts into the sauce.
Return the chicken to the pan and cook 2–4 minutes more until the chicken is fully cooked and warmed through, spooning sauce over the pieces.
Garnish with minced fresh parsley if desired and serve immediately.
