In a large bowl, combine zucchini, beef, breadcrumbs, garlic, onion, egg, feta, oregano, salt, and pepper. Mix well and make 5 equal patties.
To grill indoors: Heat a large nonstick grill pan or skillet on high heat. When hot, lightly spray oil. Add burgers to the pan and reduce the heat to medium. Cook on one side ~4-5 minutes, then flip. Cook ~4-5 minutes.
To grill outdoors: Cook the burgers on medium heat ~5 minutes on each side.
In a medium bowl whisk the vinegar, oil, salt, and pepper. Add the remaining salad ingredients and mix.
To serve, place the burger on a dish and top with 1 cup of salad.