Meat: In a large mixing bowl, combine the ground meat, parsley, mint, basil, oregano, garlic, roasted red peppers, breadcrumbs, feta, egg, salt, and pepper. Squish together with your hands (or lightly with a meat chopper) until combined. Divide into 5 equal portions and form into patties, pressing a thumb imprint into the center of each.
Cook Patties: Heat grill over medium-high heat (or use a cast iron skillet, to cook on stovetop) and grease well. Add patties and cook for a few minutes on each side, flipping once, until cooked through (165 degrees F). Remove to a plate and cover to keep warm.
Cook onions: Add onions to grill and cook for 3-4 minutes, until slightly charred.
Feta Aioli: Combine all the ingredients in a bowl and stir until well combined.
Assemble: Top burger buns with aioli, then greek burger patty, onion, arugula, and more sauce. Apply top bun, and enjoy.
Serve with: Tomato Cucumber Salad , Burrata Salad, or Fries.
