Start by placing the chicken breasts between two sheets of plastic wrap or parchment paper. Use a meat mallet or rolling pin to gently pound the chicken to an even thickness, about 1 inch.
On a plate, spread out the all-purpose flour. Season it generously with coarse salt and freshly cracked pepper. Dredge each chicken breast in the flour mixture, ensuring both sides are coated well.
In a large skillet, heat 4 tablespoons of olive oil over medium-high heat. Once hot, add the chicken breasts and cook for about 5-7 minutes on each side until golden brown and cooked through.
Remove the chicken from the skillet and keep warm. In the same skillet, add the sliced garlic and sauté for about 1 minute until fragrant.
Pour in the chicken stock and scrape up any browned bits from the bottom of the skillet. Let it simmer for about 2-3 minutes.
Reduce heat to low, add the unsalted butter and lemon juice, stirring until the butter is melted and the sauce is well combined. Adjust seasoning with salt and pepper if needed.
Return the chicken to the skillet, spooning the sauce over the top. Allow to warm through for another minute. Garnish with parsley if desired, then serve immediately.