Heat olive oil in a small skillet over medium heat. Cook and stir onions in the hot oil until tender and lightly browned, about 15 minutes; transfer to a large bowl.

Mix bread crumbs, Worcestershire sauce, Dijon mustard, garlic, poultry seasoning, ground mustard, pepper, and salt with the onion. Break the turkey into small pieces into the bowl; mix with the bread crumb mixture until evenly combined. Shape the turkey mixture into 12 patties; wrap in plastic wrap and refrigerate at least 20 minutes.

Coat a nonstick skillet with cooking spray; heat over medium heat.

Cook the patties in the hot skillet until no longer pink in the center and the juices run clear, 4 to 5 minutes per side. An instant-read thermometer inserted into the center should read at least 165 degrees F (74 degrees C).