Place each piece of chicken on a cutting board, cover with plastic wrap and pound to 1/2 inch or less thickness using a meat mallet.
Season both sides of the chicken breast with fine sea salt and freshly ground pepper.
Place flour in a shallow dish or pie plate. Dredge each piece of chicken in flour and shake off excess.
Melt 1 tablespoon butter in a large skillet over medium-high heat. Add 1 tablespoon oil to pan; swirl to coat. Add chicken to pan, working in batches, sauté 4 minutes on each side or until done. Remove chicken from pan; keep warm.
Heat remaining 1 tablespoon oil in pan. Add shallots, cooking for 2-3 minutes. Add garlic, cooking for 1 minute.
Add wine, bringing to a low simmer and scraping pan to loosen browned bits. Cook until liquid reduces by half.
Add broth to pan bringing back to a low simmer. Cook until reduced by half, approximately 5 minutes.
Remove from heat and whisk in remaining 1 1/2 tablespoons butter, lemon slices, capers and parsley.
Add chicken back to pan, spoon sauce over pieces and allowing to rewarm.
Serve over cooked pasta.
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