Instructions

Rinse and drain 3 pounds trimmed chicken drumsticks. Transfer to large bowl. Add 2½ cups milk and toss to coat. Arrange chicken in even layer, making sure all chicken is submerged in milk. Cover and refrigerate for 1 hour.
Drain and thoroughly rinse chicken until water runs clear. Clean and dry bowl. 
Using sharp knife, make 4 to 6 slashes in each drumstick (each slash should reach bone). Pat chicken dry with paper towels and transfer back to bowl. 
Add ¼ cup extra-virgin olive oil, ½ teaspoon fine salt, and ½ teaspoon pepper, and toss chicken to coat. Cover and refrigerate for at least 1 hour or up to overnight.
Meanwhile, whisk ¼ cup honey, 2 tablespoons soy sauce, 2 tablespoons distilled white vinegar, 2 tablespoons sugar, ½ teaspoon salt, and ½ teaspoon pepper together in small bowl. Set sauce aside.
Remove chicken from fridge and toss again to coat in oil that has settled in bowl. Working with 1 drumstick at a time, stretch skin to evenly cover meat, then arrange skin-side down in 12‑inch nonstick skillet. Drizzle any remaining oil left in bowl over chicken. 
Cook over medium-high heat, turning chicken occasionally, until spotty golden brown, about 10 minutes. 
Reduce heat to medium, cover, and continue to cook, turning chicken occasionally, until it registers at least 185 degrees, about 20 minutes. 
Spoon 6 tablespoons finely chopped garlic into spaces between drumsticks where oil has pooled. Cook, spreading garlic into skillet with back of a spoon, until fragrant, about 30 seconds. Gently toss chicken until evenly coated with garlic. 
Add reserved sauce, stirring in any browned bits in skillet. Increase heat to medium-high and cook, continuously coating and basting chicken in sauce, until sauce has thickened, about 2 minutes.
Stir in butter until sauce has thickened into glaze, about 30 seconds. Serve immediately.