Pound chicken breasts to 1/2-inch thickness. Pat dry and season with salt and pepper.
Heat olive oil in a large skillet over medium-high heat. Add chicken and cook for 6-7 minutes per side until golden and cooked through. Remove from skillet and set aside.
Reduce heat to medium and add butter, shallot, garlic, salt, and pepper to the skillet. Cook for about a minute until fragrant.
Sprinkle flour over the mixture and stir, cooking for another minute. Slowly add half-and-half and chicken broth, stirring continuously.
Bring to a boil, then reduce to a simmer. Return chicken to the skillet and cook for 3-4 minutes until the sauce thickens. Stir in lemon juice.
Garnish with parsley and lemon slices before serving.
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Notes
Store leftovers in an airtight container in the refrigerator for up to 3 days.