Season chicken with 1 teaspoon salt and ¼ teaspoon black pepper. Working one at a time, dredge chicken in flour.
Melt 2 tablespoons butter in a large skillet over medium high heat.
Add chicken and cook, flipping once, until cooked through, about 4 minutes on each side. Set aside and keep warm.
Melt 2 tablespoons butter in the skillet. Add shallots, and cook, stirring frequently, until fragrant, about 2 minutes. Add garlic and sauté for 20 seconds (make sure not to get too dark). Stir in chicken broth, and lemon juice. Cook, stirring occasionally, until slightly reduced, about 5 minutes.
Gradually whisk in heavy cream until slightly thickened, about 3-4 minutes; season with remaining salt and pepper. Add remaining 1 tablespoon butter and capers (if using) to the sauce, stir and add chicken back into the pan. Sprinkle parsley and serve immediately. Enjoy!
