Combine onion, garlic, rosemary, pepper, and curry powder together in a large bowl. Add the turkey last and mix with your hands just until evenly combined. Do not overmix.
Divide turkey mixture into quarters (use a kitchen scale if you want to be precise) and shape into balls.
Flatten each ball into a patty ¾"-1" thick, approximately 4" wide.
Use your thumb to make indentations on the flat sides of each patties to help them stay flat while cooking.
Heat 1-2 tablespoon oil in a cast iron pan over medium heat. You'll know it's ready when a droplet of water flicked into the pan sizzles and evaporates immediately.
Generously salt the outside of each patty before placing it in the pan. Holding the patty in the palm of your hand, sprinkle salt over the side facing up, then place the patty salt-side down in the skillet. Repeat for each patty. Cook 5 minutes.
Just before flipping the patties, salt the tops. Then flip and cook an additional 4-5 minutes on the second side.
Serve on your favorite burger buns with your favorite burger toppings.