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In a large skillet, heat oil over medium-high. Add chicken thighs, season with salt and pepper, and cook, stirring once, until meat is golden brown, 5 minutes. With a slotted spoon, transfer to a slow cooker, leaving as much oil behind as possible. Repeat with chicken breasts.
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To skillet, add onion, garlic, and bell pepper and cook over medium, stirring constantly, until onion is translucent, 6 minutes. Add 1/4 cup water and cook, stirring and scraping up browned bits from skillet, 5 minutes. Season with salt and pepper and transfer to slow cooker.
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To slow cooker, add crushed tomatoes, hot-pepper sauce, Worcestershire, mustard, and molasses; stir to combine. Cover and cook on high until chicken is very tender, 4 hours. Shred chicken and season to taste with salt and pepper. Serve on buns.