Heat 1 tablespoon oil in a large skillet over medium-high heat.
Season the chicken pieces with salt and pepper and cook in the skillet until lightly browned on all sides, about 10 to 15 minutes.
Transfer the browned chicken to the slow cooker.
Add carrots, sliced green onions (reserve some for garnish), sliced celery, minced ginger, minced garlic, bean sprouts, soy sauce, red pepper flakes, drained chopped water chestnuts, chicken stock, and sugar to the slow cooker; stir to combine.
Cover and cook on HIGH for 3 to 4 hours or on LOW for 6 to 10 hours, until the chicken is cooked through and tender.
About 10 minutes before serving, whisk the cornstarch and cold water together in a small bowl until smooth, then stir the slurry into the slow cooker.
Stir occasionally until the sauce thickens, about 10 minutes.
Meanwhile, cook chow mein noodles (or prepare rice) according to package instructions.
Mix the cooked noodles or rice into the chicken mixture and stir until combined.
Serve immediately, keeping on warm if needed, and garnish with reserved sliced scallions and optional red pepper flakes or toasted sesame seeds.
