Start by patting the chicken breasts completely dry with paper towels to help achieve a good sear. Season both sides generously with kosher salt and black pepper.

Warm the olive oil in a large skillet over medium-high heat until shimmering. Add the chicken breasts in a single layer—working in batches if your skillet isn’t large enough—and sear undisturbed for 6 to 7 minutes until the bottom develops a deep golden crust. Flip and cook the second side for another 6 to 7 minutes. Once browned and cooked through, transfer the chicken to a plate and set aside.

Lower the heat to medium and add the butter to the same skillet. Once melted, stir in the chopped shallot and minced garlic along with 1/2 teaspoon salt and 1/4 teaspoon pepper. Sauté for about a minute until fragrant and just beginning to soften.

Sprinkle in the flour and stir to coat the aromatics evenly. Cook for another minute to eliminate any raw flour taste.

Gradually pour in the half-and-half (or milk) and chicken broth while whisking constantly to remove any flour lumps. Scrape up any golden bits stuck to the bottom of the pan for extra flavor. Bring the mixture to a gentle boil, then reduce to a simmer.

Return the seared chicken to the pan, nestling it into the creamy sauce. Simmer for 3 to 4 minutes until the sauce thickens slightly and clings to the back of a spoon, and the chicken is warmed through.

Stir in the lemon juice for a bright, tangy finish. Garnish with freshly chopped parsley and lemon slices. Serve immediately with your favorite sides.