Rinse and drain 3 pounds trimmed chicken drumsticks.

Place in a large bowl, add 2 cups whole milk, and toss to coat.

Arrange drumsticks in an even layer, ensuring all are submerged. Cover and refrigerate for 1 hour.

Drain chicken and rinse thoroughly until water runs clear. Clean and dry the bowl.

Using a sharp knife, make 4–6 slashes in each drumstick, cutting to the bone. Pat dry with paper towels and return to the bowl.

Add 3 tablespoons extra-virgin olive oil, ¾ teaspoon fine salt, and ¾ teaspoon pepper. Toss to coat, cover, and refrigerate for at least 1 hour or overnight.

In a small bowl, whisk together 3 tablespoons honey, 1½ tablespoons soy sauce, 1½ tablespoons distilled white vinegar, 1½ tablespoons sugar, ¼ teaspoon salt, and ¼ teaspoon pepper. Set sauce aside.

Remove chicken from the refrigerator and toss again in the settled oil. Stretch the skin to cover each drumstick evenly.

Place skin-side down in a 12-inch nonstick skillet. Drizzle any remaining oil from the bowl over the chicken.

Cook over medium-high heat, turning occasionally, until spotty golden brown, about 10 minutes.

Reduce heat to medium, cover, and cook, turning occasionally, until the chicken reaches at least 185°F, about 20 minutes.

Add 5 tablespoons finely minced garlic to the oil pools between drumsticks.

Cook, spreading garlic with a spoon, until fragrant, about 30 seconds. Gently toss chicken to coat evenly with garlic.

Pour in the reserved sauce, scraping up browned bits from the skillet.

Increase heat to medium-high and cook, continuously basting chicken, until the sauce thickens, about 2 minutes.

Stir in 2 tablespoons salted butter until the sauce forms a glaze, about 30 seconds. Serve immediately.