1/4cupchopped fresh parsleyplus additional for serving
Split each chicken breast in half horizontally to create two thinner pieces of chicken. I like to do this by carefully placing my hand on top to give myself a feel for whether or not I am slicing the chicken evenly. To make the chicken easier to slice, you can place it in the freezer for 10 to 15 minutes prior to cutting. Sprinkle the chicken on both sides with salt and pepper.
Place the flour in a shallow bowl. Lightly dredge each piece of chicken on both sides with the flour.
In a large, sturdy skillet, heat olive oil over medium to medium-high heat. Add 2 tablespoons of the butter. Once the butter has melted, carefully lower a single layer of chicken pieces into the skillet (angle the chicken away from you as you set it down), ensuring they do not touch each other in the pan. Cook on both sides until golden brown and cooked through, about 3 minutes per side.
Transfer the chicken to a plate. Repeat with remaining batch(es). If at any point the pan seems dry, drizzle in a little more oil.
Reduce the pan heat to medium-low. Add the shallot to the now-empty pan. Cook, stirring occasionally, until the shallot is lightly caramelized, about 2 to 3 minutes.
Add the wine and broth and return the heat to medium. Let simmer, stirring often, until it is reduced by half, about 3 minutes.
Reduce the heat to low. Add the lemon zest (I zest it right over the pan), lemon juice, capers, and remaining 2 tablespoons butter. Stir to combine, then season with more salt and pepper to taste. Stir in the parsley. Serve the chicken with the sauce spooned generously all over the top. Garnish with additional parsley as desired.
TO STORE: Refrigerate chicken in an airtight storage container for up to 3 days.
TO REHEAT: Gently rewarm leftovers in a skillet on the stovetop over medium-low heat or in the microwave.
TO FREEZE: Freeze chicken in an airtight, freezer-safe storage container for up to 3 months. Let thaw overnight in the refrigerator before reheating.