In a large non-stick skillet, over medium-high heat, warm the olive oil. Add in the ground turkey and onions; cook until the onions are softened and no pink remains in the turkey, about 3 minutes. Drain off all the grease.
Stir in garlic powder, ketchup, mustard, and brown sugar. Mix well. Season with the salt and pepper. Stir in the Dirty Dill Baby Dills and mix to combine. Transfer sloppy joe mixture to a bowl and set aside; cover to keep warm.
Wipe out your skillet and return pan to medium heat. Spread butter over one side of a slice of bread. Place butter side down into the skillet, top with a little cheese, generous amount of sloppy joe mixture, and additional cheese, and finish with another buttered slice of bread, butter side up. Option to layer additional Dirty Dills in the sandwich.
Cook in the skillet until lightly browned on the bottom, about 1-2 minutes, and flip over. Press down to flatten slightly, so the cheese can melt. Continue cooking until the other side has browned and the cheese has melted, another 1-2 minutes or so. Repeat with remaining sandwiches. Serve warm.