If using wooden skewers, place them in water to soak for at least 30 minutes while you prepare the meat.
In a large bowl, combine the ground turkey, minced onion, minced garlic, chopped parsley, bread crumbs, allspice, coriander, paprika, chili powder, and salt and pepper to taste. Mix until evenly blended, taking care not to overwork the meat.
Divide the mixture into 10 equal portions (about 1/4 cup each).
Shape each portion into a firm, log-shaped oval (about 3–4 inches long and roughly 1 inch thick). Place the shaped koftas on a cookie sheet.
Refrigerate the shaped koftas on the cookie sheet for at least 30 minutes to firm up (this also allows time for wooden skewers to finish soaking).
Preheat your grill to medium-high and set up for indirect heat if possible (one cooler side and one hotter side).
When ready to cook, carefully thread each log onto a skewer lengthwise. Leave a little space at the ends for turning.
Place the skewers on the grill over the indirect (cooler) side, cover, and cook for 12–15 minutes, turning once halfway through, until mostly cooked through.
Move the skewers over to the direct (hotter) side and finish grilling 3–4 minutes per side, turning occasionally, until the koftas are browned and an instant-read thermometer inserted into the center reads 165°F (no pink remaining).
Remove from the grill and let the kebabs rest 3–5 minutes before serving.