Whisk together the honey mustard, chili sauce, eggs, and sea salt in a bowl. Place the chicken drumsticks in a large, sealable plastic bag; pour the marinade over the chicken and seal the bag. Allow to chill in refrigerator at least 4 hours.
Preheat an oven to 350 degrees F (175 degrees C).
Place the bread crumbs in the bottom of a wide dish; dredge the marinated chicken in the bread crumbs to coat. Heat the vegetable oil in a large, deep pan over medium-high heat. Gently lie the breaded chicken into the hot oil until golden brown, 5 to 7 minutes, turning once if needed to get even coloring; transfer to a baking sheet.
Cook the chicken legs in the preheated oven until no longer pink at the bone and the juices run clear, about 30 minutes. An instant-read thermometer inserted near the bone should read 165 degrees F (74 degrees C).
