Combine the meat, red onion, parsley, pine nuts, sun-dried tomatoes, garlic, feta cheese, salt and Greek seasoning in a mixing bowl. Work with your fingers until the mixture is thoroughly combined. Form into 4 patties. Grill or pan fry over medium-high heat for 2-3 minutes on each side or according to desired doneness (is using poultry or pork, make sure it's thoroughly cooked through). If you're cooking them on the stovetop, I like to use the Lodge Cast Iron Grill Pan to get those pretty grill marks.
Arrange some arugula leaves on the bottoms of each hamburger bun and place the patties on top. Top with tomatoes, red onions, tzatziki sauce, and crumbled feta cheese. Place the top bun on each burger and serve immediately with extra tzatziki sauce.