Using a large hole box grater, shred zucchini; transfer to a clean kitchen towel.
Gather corners of towel and squeeze tightly to release excess liquid. (When you think you’re done, squeeze a bit more.) Shredded zucchini should measure about 2 cups (8 ounces in weight).
Combine 1 cup shredded and squeezed zucchini, turkey, ½ cup yogurt, bread crumbs, parsley, oil, oregano, Worcestershire, 1 ½ teaspoons garlic, ½ teaspoon salt, and ¼ teaspoon red pepper flakes.
Divide meat into 4 equal portions.
Gently form each into a ball, then lightly flatten into 1-inch-thick burger patties. Press finger through center of patties (this helps keep the patties flat during cooking) and transfer to a plate; chill patties at least 15 minutes or up to 4 hours.
For the sauce, combine remaining 1 cup shredded and squeezed zucchini, remaining 1 cup yogurt, remaining ½ teaspoon garlic, dill, vinegar, ½ teaspoon salt and ¼ teaspoon black pepper; season with additional salt and pepper to taste.
Heat a large cast-iron skillet over medium for 5 minutes. Brush with a teaspoon or so of grapeseed oil to coat.
Transfer burger patties to pan and cook, without moving, until bottom sides are dark brown and crusted, 3–4 minutes. Flip burgers and cook until charred and crusted, 4–5 minutes more and an instant-read thermometer register 160ºF. (Total cook time will be 9–10 minutes.)
Transfer burgers to a plate and let rest 5–10 minutes.
Serve burgers with tzatziki and orzo salad or on a bun with tzatziki, lettuce, tomato and crumbled feta.