Prep the chicken: Trim excess fat from chicken. If using large breasts, cut in half for even cooking. Pat dry.
Make the sauce base: In a bowl, whisk together pineapple with juice, ketchup, soy sauce, brown sugar, rice vinegar, garlic, and ginger until smooth.
Load the slow cooker: Place chicken in the slow cooker.
Scatter the bell pepper on top if using. Pour the sauce mixture over everything, making sure the chicken is mostly submerged.
Cook low and slow: Cover and cook on Low for 4 to 5 hours or High for 2.5 to 3.5 hours, until the chicken is tender and easily shreds with a fork. Avoid lifting the lid too often.
Shred the chicken: Transfer chicken to a plate and shred with two forks.
Skim any excess fat from the sauce if needed.
Thicken the sauce: In a small bowl, mix cornstarch and water to make a slurry. Stir the slurry into the sauce in the slow cooker. Cover and cook on High for 10 to 15 minutes until the sauce is glossy and slightly thickened.
Combine and finish: Return shredded chicken to the slow cooker, toss to coat in the sauce, and let it warm through for 5 minutes.
Taste and adjust seasoning: add a splash of soy for salt, a pinch of brown sugar for sweetness, or vinegar for tang.
Serve: Spoon the chicken and sauce over hot rice or noodles. Garnish with sliced green onions and sesame seeds.