In a medium pan on medium heat, warm olive oil. Add red onion and cook for 2-3 minutes until tender, then add garlic and cook for an additional minute until fragrant. Finally, add chopped spinach and a pinch of salt and cook until spinach is wilted and tender. Remove from the heat and set aside, allow to cool slightly. (Although you can add these ingredients to the burgers raw, cooking them lightly prior to mixing them with the ground turkey helps to enhance the flavour and texture.)
In a large bowl, add ground turkey and red onion, garlic and spinach mixture, crumbled feta, a pinch of salt, and pepper. Using your hands, mix the ingredients until well combined, and then divide and shape into 4 evenly sized burger patties.
Heat a grill or grill pan to medium-high heat, then add patties and cook for 5-6 minutes per side until cooked through to an internal temperature of 165ºF.
While the burgers are cooking, prepare the yogurt sauce. Add the Greek yogurt, parsley, salt, and pepper to a small bowl or jar and stir until well combined. Set aside.
Once the burgers are cooked, remove them from the grill and assemble them on buns with yogurt sauce and toppings of your choice.
Any leftover burger patties can be stored in an airtight container in the fridge for up to 5 days.