To a food processor, add in feta cheese, 2 tbsp olive oil, Greek yogurt and lemon juice. Pulse until creamy and lowly add in 1-2 more tablespoons of extra-virgin olive oil if a creamier texture is desired. Feta spread can be made 1-2 days in advance and refrigerated.
On preheated grill over medium heat, place burgers 4 inches from heat source for 9-10 minutes per side (turning twice) and until fully cooked to 165 F.
Remove burgers from grill. Top each burger with whipped feta, and your favorite burger toppings!