1. Slice thick chicken breasts horizontally into thinner cutlets. Pat dry with paper towels, then season both sides with kosher salt and black pepper. Dredge each piece lightly in flour, shaking off any excess.

2. Heat olive oil and 1 tablespoon of the butter in a large skillet over medium-high heat. Add the floured chicken in a single layer and sear for 2–3 minutes per side until lightly golden (do this in batches if needed). Transfer browned chicken pieces to the crockpot.

3. Reduce the skillet heat to medium and add the minced garlic. Cook for about 30 seconds, stirring constantly, until fragrant. Pour in the white wine (or extra broth) and scrape up any browned bits from the bottom of the pan.

4. Add the chicken broth, fresh lemon juice, Italian seasoning, and capers to the skillet. Stir and let the mixture bubble for 1 minute, then carefully pour the sauce over the chicken in the crockpot.

5. Cover and cook on low for 3–4 hours or on high for 1 1/2–2 1/2 hours, until the chicken is cooked through and very tender. Avoid lifting the lid too often so the crockpot can maintain its heat.

6. When the chicken is done, whisk the cornstarch and cold water together in a small bowl until smooth. Gently transfer the chicken to a plate. Stir the cornstarch slurry into the hot cooking liquid in the crockpot, then stir in the remaining 1 tablespoon butter.

7. Turn the crockpot to high, cover, and cook the sauce for about 10 minutes, stirring once or twice, until slightly thickened and glossy.

8. Return the chicken to the crockpot or arrange it on a serving platter. Spoon the lemon-garlic caper sauce over the top, sprinkle with chopped parsley, and garnish with lemon slices. Serve warm over pasta, rice, or mashed potatoes.