Step 1: In a small saucepan over medium heat, bring the apple cider to a boil. Reduce the heat and simmer until the liquid has reduced to about 1/2 cup (approximately 15-20 minutes). It should be syrupy.
Step 2: While the cider reduces, preheat your oven to 400°F (200°C). Pat the chicken drumsticks dry with paper towels and season them with salt, pepper, and smoked paprika.
Step 3: Heat olive oil in a large oven-safe skillet over medium-high heat. Sear the drumsticks on all sides until golden brown, about 2-3 minutes per side.
Step 4: In a small bowl, whisk together the reduced apple cider, Dijon mustard, apple cider vinegar, minced garlic, and grated ginger.
Step 5: Brush a generous amount of the cider glaze over the seared drumsticks. Place the skillet (or transfer to a baking sheet) into the oven.
Step 6: Roast for 30-35 minutes, basting the chicken with more glaze every 10 minutes until the internal temperature reaches 165°F (74°C) and the glaze is sticky and darkened.
Step 7: Remove from the oven and let the apple cider glazed chicken drumsticks rest for 5 minutes before serving with any remaining glaze poured over the top.