Blend the cilantro, sauce garlic, mayonnaise, cottage cheese, and vinegar in a food processor or with an immersion blender in a tall glass, then refrigerate for at least 30 minutes before seasoning with salt and pepper. The dip should look creamy and taste bright once chilled.

Grate the zucchini onto a clean kitchen towel or paper towel, sprinkle it with a small pinch of kosher salt, and squeeze out the liquid. The shreds should feel damp rather than wet enough to drip.

Mix the squeezed zucchini with the ground chicken, minced garlic, chives, 1/2 teaspoon kosher salt, and 1/4 teaspoon black pepper, then shape into 8 to 12 patties about 2 to 3 inches across. Each flattened patty should hold its shape when lifted.

Heat the oil in a large skillet over medium-high heat and cook the patties for 4 minutes per side, lowering the heat to medium and covering for 2 minutes if they brown before the centers cook through. The exteriors should be browned and the centers cooked through.

Serve the warm patties with the chilled cilantro sauce alongside or spooned over them. The cool, tangy sauce balances the savory crust.