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 sugar dissolves and the marinade is uniform.
Season the drumsticks with salt and pepper to taste, then place them in a large resealable bag and pour in the marinade. Seal the bag and refrigerate for a few hours or up to overnight.
Transfer the marinated chicken 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 reaches 165°F (74°C).
Carefully remove the drumsticks from the slow cooker and arrange them on a rimmed baking sheet.
Place the sheet under a preheated oven broiler and broil just until the skin crisps and caramelizes, watching closely to avoid burning.
Let the drumsticks rest briefly, then serve. Optionally garnish with green onions, jalapeño slices, and sesame seeds if desired.