Heat 1 tablespoon butter in a cast-iron or nonstick skillet over medium-high heat.
Season the chicken breasts with salt and pepper and sear in the hot skillet until golden, about 3 minutes per side.
Transfer the seared chicken to the 6-quart slow cooker and place the remaining 4 tablespoons butter, divided into 4 pieces, on top of the breasts.
Add the dried basil, crushed red pepper flakes, lemon juice, and lemon zest to the slow cooker, over the chicken.
Cover and cook on LOW for 3 1/2 hours (or on HIGH for just under 2 hours) until the chicken is cooked through.
In a small bowl, stir 1 tablespoon of the half-and-half into the cornstarch until smooth, then whisk that into the remaining half-and-half. Stir in the chicken base and the rinsed, drained capers.
Pour the half-and-half mixture into the slow cooker, stir gently to combine with the cooking juices, cover, and cook on HIGH for 1 more hour to thicken and finish the sauce.
Check seasoning and serve the chicken with the creamy lemon-caper sauce spooned over it.