In a medium bowl, whisk together the honey, soy sauce, minced garlic, rice vinegar, tomato paste, sesame oil, red pepper flakes, and black pepper until the honey is fully blended into the sauce and everything is smooth.

Pat the chicken drumsticks dry with paper towels. Drying the surface helps the sauce cling rather than slide right off. Arrange the drumsticks in the slow cooker insert, stacking them slightly if needed.

Pour the honey garlic sauce evenly over the drumsticks, turning each one so it gets coated on all sides. Cover the slow cooker and cook on LOW for 5 to 6 hours, or on HIGH for 3 hours. The chicken is done when the meat pulls away from the bone easily and an instant read thermometer reads 165 degrees F.

When the chicken is cooked through, preheat your oven broiler to high and line a sheet pan with foil. Use tongs to transfer the drumsticks to the prepared sheet pan in a single layer. Reserve the cooking liquid in the slow cooker.

Pour the reserved cooking liquid into a small saucepan and bring it to a simmer over medium heat. Let it cook for 5 to 8 minutes, stirring occasionally, until it reduces by about a third and is thick enough to coat a spoon. If you want it even thicker, whisk the cornstarch with 1 teaspoon of cold water, stir it in, and cook for 1 more minute.

Brush the reduced sauce generously over the drumsticks on the sheet pan. Slide the pan under the broiler and broil for 4 to 5 minutes, watching closely, until the glaze is caramelized and the skin is lightly charred at the edges. Every broiler runs different, so start checking at 3 minutes.

Transfer the drumsticks to a serving platter, drizzle with any remaining reduced sauce, and top with sesame seeds and sliced green onions. Serve over white rice with steamed broccoli on the side.