Pat the chicken dry and season with salt and pepper. Dredge lightly in flour and shake off excess.
Heat olive oil and butter in a large skillet over medium-high heat. Cook chicken 3–4 minutes per side until golden and cooked through. Transfer to a plate and tent with foil.
Lower heat to medium, add garlic and sauté briefly. Add broth and deglaze the pan, scraping browned bits. Reduce by half.
Stir in chicken broth, lemon juice, and capers. Simmer 3–4 minutes to reduce slightly.
Reduce heat to low, whisk in heavy cream and simmer until thickened. Whisk in cold butter pieces for gloss.
Return chicken to the pan, spoon sauce over, warm through 1–2 minutes, garnish with parsley, and serve over pasta or rice.
Notes
Do not overcrowd the pan when searing—work in batches if necessary.
Use fresh lemon juice for the brightest flavor.
If the sauce is too thick, thin with a splash of chicken broth.
To make lighter, substitute half-and-half for heavy cream.