Place the turkey breast in a 6-quart slow cooker, cover, and cook on the low-heat setting for 6 to 8 hours (depending on the size of the breast) or until a meat thermometer registers 165°F. Remove the turkey from the cooker and let cool slightly on a cutting board. Pour off any liquid from the slow cooker crock.
Cut or shred the turkey into smaller pieces and return them to the slow cooker. Arrange the broccoli and peppers on top of the turkey. In a bowl stir together the marmalade, barbecue sauce and soy sauce, and pour it over the turkey and vegetables and stir to combine. Cover the slow cooker and cook on the high-heat setting for 30 minutes. Serve turkey and vegetables over brown rice.