Preheat the oven to 350 degrees F (175 degrees C). Line a rimmed baking sheet with aluminum foil. Heat oil in a large skillet over medium heat. Add onion and cook until tender and starting to brown, 3 minutes.
Add garlic and cook until fragrant, 1 minute. Remove from skillet and let cool for 5 minutes.
Combine bread crumbs and milk in a large bowl. Add eggs, parsley, vinegar, salt, oregano, mint, and pepper; stir to combine.
Add cooled onion mixture and ground beef. Mix just until combined. Do not overmix.
Shape into 12 (3/4-inch-thick) patties and arrange on the prepared baking sheet.
Bake in the preheated oven until an instant-read thermometer inserted into the center of a patty registers 160 degrees F (71 degrees C), about 20 minutes.
Serve warm with lemon wedges and Greek style potatoes or an easy Greek salad.
