Pulse the rolled oats in a small food processor 5 to 6 times until they look like coarse flour. Skip this step if using panko.

In a large mixing bowl, combine the ground turkey, egg, ground oats, feta, garlic, smoked paprika, onion powder, salt, and pepper. Mix with your hands just until combined, 20 to 30 seconds. Overmixing makes the patties dense.

Divide the mixture into 4 portions, about 170 g each, and shape into patties 2 cm / 3/4-inch thick. Press a shallow dimple into the center of each with your thumb so they cook flat instead of doming.

Heat the olive oil in a 30 cm / 12-inch cast-iron skillet over medium heat until it shimmers.

Add 2 patties at a time, leaving space between them, and cook for 5 to 6 minutes per side without pressing down, until deeply browned and an instant-read thermometer reads 165 F / 74 C at the center. Transfer to a plate and tent loosely with foil.

Repeat with the remaining 2 patties, adding a little more oil to the skillet if it looks dry.

Whisk the Greek yogurt, smoked paprika, lemon juice, grated garlic, and a pinch of salt in a small bowl until smooth.

Split the buns and toast cut-side down in the same skillet for 1 to 2 minutes until golden.

Build each burger with the bun bottom, lettuce, a patty, a spoonful of yogurt sauce, tomato, red onion, and avocado if using. Close with the top bun and serve right away.