Heat a large nonstick skillet over medium-low heat. Add the EVOO (1 turn of the pan) and the butter. When the butter melts, add the My Big, Fat Greek Burger chopped red onion and chopped garlic and cook for 5 minutes. Transfer the onion and garlic to a large bowl to cool.
Wring the thawed spinach dry by twisting it in a clean kitchen towel over your sink. Break up the block of spinach as you add it to the cooled onion and garlic. Season with 1 teaspoon of the oregano (one-third palmful). Add the ground chicken and feta, then the grill seasoning and a healthy drizzle of EVOO. Mix it all together, then divide the mixture with the side of your hand into 4 equal sections. Form 4 patties, each 1 inch thick. In the same skillet, cook the patties over medium-high heat for 5 minutes on each side.
Combine the sliced cucumber and tomato with the sliced red onion, arugula and hot pepper rings. Dress with half of the lemon juice and EVOO to taste and season with salt and pepper; reserve.
Toast the rolls. Place the chopped cucumber in a food processor with the crushed garlic, yogurt, the remaining oregano and the remaining lemon juice. Add a little salt and process until smooth. Transfer to a small dish. Rinse out the bowl and return it to the base.
Place the roasted red peppers, parsley and olives in the food processor, season with salt and pepper and process to a paste. Remove the blade and reserve the paste in the processor bowl.
Slather the roll bottoms with the yogurt sauce. Place the cooked burgers on the sauce and top with the salad. Slather the roll tops with the red pepperolive paste and serve with chips of your choice.