Combine all of the ingredients except the bread and relish in a large bowl and mix until evenly incorporated. Form into 4 patties.2.
Heat a grill pan or outdoor grill to medium (about 350°F to 450°F). Once the grill is hot, cook the burgers about 10 minutes per side, or until the juices run clear and the patties are firm to the touch.3.
Place the burgers on the buns, top with relish, and serve.
Cut cleaned cucumbers into small dice and place in a colander set over a mixing bowl. Sprinkle with 1 teaspoon of the kosher salt and toss to coat. Weight down cucumbers by setting a plate on top, and let drain for 10 minutes. Occasionally press down on the plate to extract excess water.2.
Meanwhile, combine yogurt, vinegar, parsley, mint, sugar, coriander, cumin, cayenne, and remaining 1/2 teaspoon salt in a medium mixing bowl, stirring until evenly combined.3.
Blot cucumbers with paper towels, add to yogurt mixture, and stir to combine. Taste and adjust seasoning as desired.