Whisk together the soy sauce, chicken broth, sweet chili sauce, Sriracha, brown sugar, lime juice, minced garlic, and grated ginger in a mixing bowl until the sugar dissolves.
Season the drumsticks lightly with salt and black pepper to taste.
Place the drumsticks in a large resealable bag or container and pour the marinade over them. Seal and refrigerate for a few hours or up to overnight to marinate.
Transfer the drumsticks and any remaining marinade to a 6-qt slow cooker. Cover and cook on LOW for 5–6 hours or on HIGH for 3–4 hours, until the chicken is cooked through.
Carefully remove the drumsticks to a rimmed baking sheet. If desired, place under a preheated oven broiler and broil until the skin is crispy and slightly charred, watching closely to avoid burning.
Use a meat thermometer to ensure the thickest part of the drumstick reaches 165°F (74°C) before serving.
Garnish as desired with green onions, jalapeño slices, and sesame seeds and serve.