In a medium bowl, combine the chicken, broccoli, cheddar, Parmesan, garlic powder, Greek yogurt, Dijon mustard, and salt & pepper.
Divide the mixture evenly between four of the bread slices, and top with another slice of bread.
Melt butter and olive oil in a pan over medium-low heat.
Cook the sandwiches for about 3-4 minutes per side, or until golden brown and the cheese has melted. Covering the pan with a lid during cooking will help the inside get all warm and gooey before the bread gets too browned.