Pat chicken thighs dry with a paper towel; season with salt and pepper. Place chicken thighs skin-side up on the grill pan of a Countertop Induction Oven (CIO).
Cut larger potatoes in half so all potatoes are about the same size. Place potatoes in a bowl and drizzle olive oil over potatoes; season with salt and pepper. Place potatoes on the grill pan with chicken.
Place grill pan in the CIO and set to "Auto Cook 1" for 2 pounds chicken. Cook chicken until no longer pink and an instant-read thermometer inserted near the bone reads 165 degrees F (74 degrees C), about 24 minutes.
Combine ketchup and bourbon in a small saucepan over medium-high heat. Whisk apple cider and cornstarch together in a small bowl until smooth; pour into ketchup mixture. Bring to a boil, whisking occasionally, until sauce is thickened, about 10 minutes. Remove sauce from heat and stir in 1/8 teaspoon black pepper; set aside to cool.
Serve chicken and potatoes with sauce on the side.