Combine the oil, thyme, brown sugar, allspice, lime juice, garlic, chile peppers, ginger, scallions, 1 1/2 teaspoons salt and 1/4 teaspoon black pepper in a food processor and pulse until smooth.
Coat the turkey legs in the jerk marinade and refrigerate at least 4 hours and up to overnight.
Preheat the oven to 425 degrees F.
Spread the turkey legs on a rimmed baking sheet and roast until the skin is golden brown all over and the turkey is cooked through (an instant-read thermometer inserted into the center of the meat, avoiding bone, should register at least 165 degrees F), 45 to 50 minutes.
Serve the turkey legs topped with the cilantro, with lime wedges on the side.