If searing, lightly dredge the chicken breasts in the flour seasoned with salt and pepper. Heat olive oil in a large skillet over medium-high heat. Sear the chicken breasts for 2-3 minutes per side until lightly golden. This step is optional but adds color/texture.

Place the seared (or unseared) chicken breasts in a single layer in the bottom of a 6-quart slow cooker.

In a medium bowl, whisk together the chicken broth, white wine (if using), and lemon juice.

Pour the liquid mixture over the chicken in the slow cooker. Cook on low for 6 hours or on high for 4 hours, until the chicken is fully cooked and easily shredded.

Carefully remove the cooked chicken and place it on a cutting board. Shred or slice the chicken and return it to the slow cooker insert.

In a small saucepan, combine the remaining cooking liquid from the crockpot with the cornstarch slurry. Heat over medium heat, stirring constantly, until the sauce thickens slightly (about 3-5 minutes).

Remove the sauce from the heat. Whisk in the cold butter pieces one at a time until fully emulsified, creating a rich, glossy sauce. Stir in the drained capers.

Pour the finished sauce over the chicken in the slow cooker and gently toss to coat. Let it sit on the 'Warm' setting for 10 minutes before serving. Garnish generously with fresh parsley.