Combine and mix together all burger patty ingredients in a bowl.
Form into 4 patties. Refrigerate patties for at least 1 hour to harden.
Heat a pan over medium heat, or use a grill. Working in batches, drizzle the inside faces of the buns with a bit of cooking oil and place them face down on the pan. Cook until toasted, a few minutes. Transfer to a serving plate.
Increase to medium-high heat or keep at medium heat to lessen the amount of smoke (it will just take longer to cook). Drizzle cooking oil over the pan. Working in batches, cook the patties until charred on both sides and the internal temperature reaches 160 F, flipping occasionally. Add more oil if the pan gets dry.
Assemble the burgers by distributing the meat and toppings among the buns. Serve hot.
Recipe printed from Savory Tooth at https://www.savorytooth.com/greek-burgers/