How to Make It
Stir together flour, salt, and pepper. Dredge chicken in flour mixture, shaking off excess.
Heat 2 tablespoons of the butter and 1 tablespoon of the oil in large nonstick skillet over medium-high. Add 3 chicken breasts; cook until golden brown, 5 to 6 minutes per side. Transfer chicken breasts to a 5-quart slow cooker, overlapping breasts. Wipe skillet clean. Repeat process with remaining 2 tablespoons butter, 1 tablespoon oil, and 3 chicken breasts.
Top chicken in slow cooker with broth, wine, capers, and lemon juice. Cover and cook on LOW until chicken is cooked through, about 4 hours.
Using a slotted spoon, transfer chicken to a serving platter. Transfer cooking liquid to a medium saucepan. Whisk together cold water and cornstarch in a small bowl until smooth. Add to cooking liquid in saucepan; stir to combine. Bring to a boil over high; cook, stirring occasionally, until reduced to 3 cups, 6 to 10 minutes. Spoon sauce over chicken. Garnish with lemon wedges.