For the peach barbecue sauce: Combine the peaches, peach nectar, ketchup, molasses, vinegar, mustard, Worcestershire sauce and adobo sauce in a deep saucepan. Bring to a boil over medium heat. Reduce the heat to low and simmer for 20 to 30 minutes, until the sauce has thickened and the flavors have melded. Puree with an immersion blender and let cool.
For the BBQ chicken: Prepare a grill for indirect cooking over medium heat.
Rub the chicken legs with the oil and sprinkle with salt and pepper. Grill the chicken over indirect heat, turning occasionally, for 25 to 30 minutes, until a meat thermometer inserted into the thickest part of the thigh registers 165 degrees F. Baste the chicken periodically using a basting brush soaked in peach brandy; do not pour brandy directly over the grill. Ten to 15 minutes before the chicken is done, brush it generously with peach barbecue sauce. Just before removing the chicken from grill, brush a final time with barbecue sauce.
Let the chicken rest for 10 to 15 minutes before serving. Serve with extra sauce on the side.