Use a vegetable peeler to remove the skin from two peaches. Cut the peaches in half to remove the pit and roughly chop into small pieces.
Add the peaches, peach nectar, chipotle peppers and their sauce, smoked paprika, soy sauce, dijon mustard, salt and pepper to a small sauce pot and bring to a boil. Turn down to low heat and simmer for 15 minutes.
In a small bowl, whisk together the cornstarch and 3 tablespoons of water. Stir the cornstarch slurry into the peach mixture, and continue cooking while stirring for 5 minutes, or until thickened.
Season the drumsticks with salt and pepper. Brush the drumsticks with the chipotle peach glaze and place them on an aluminum foil-lined sheet tray. Bake for 35 minutes, brushing with glaze halfway through.
Cut the remaining peaches in half. Remove the chicken from the oven and drizzle with 2 tablespoons of vegetable oil. Place the peach halves on the sheet tray with the drumsticks. Brush the peaches with glaze and broil for 3-5 minutes until slightly charred.
Spoon the remaining glaze over the chicken and garnish with fresh cilantro.
For the grill: Preheat the grill to high heat. Place the glazed chicken on the grill and sear for 3-4 minutes per side. Turn off one side of the grill. Brush the chicken again with glaze and move to the cool side of the grill. Close the lid and cook for 30 minutes, glazing again halfway through. Add the peaches over direct heat, cut side down for the last 3-5 minutes.
Cooks Note: The more adobo sauce you add from the chipotles, the spicier your sauce will be.