Grate the onion on the small holes of a box grater into a fine pulp. Let it sit in a fine-mesh strainer for 2 minutes to drain excess liquid. Do not squeeze dry—leave a little moisture.

In a mixing bowl, combine the ground turkey, grated onion (with any remaining liquid), breadcrumbs, egg yolk, salt, pepper, and garlic powder. Mix gently with your hands until just combined. Overmixing makes the patties dense.

Divide the mixture into 4 equal portions. Shape each into a patty about 3/4 inch thick. Press a shallow dimple in the center with your thumb to help it cook evenly and prevent puffing.

Heat the olive oil in a cast iron skillet over medium-high heat until it shimmers. Place the patties in the skillet, leaving space between them. Cook for 4-5 minutes without moving them—this builds a good crust.

Flip the patties carefully. Cook for another 4-5 minutes, or until the internal temperature reaches 165°F (74°C) on an instant-read thermometer. If you don't have a thermometer, cut into the center of one patty: the juices should run clear, and there should be no pink.

Remove the patties from the skillet and let them rest on a plate for 2 minutes. This redistributes the juices.

While the patties rest, lightly toast the buns in the same skillet (or on the grill) for about 30 seconds per side, until golden.

Assemble the burgers with your favorite toppings and serve immediately.