In a bowl, combine crab meat, mayonnaise, Dijon mustard, green onion, and parsley. Season with salt and pepper to taste. Mix gently to keep the crabmeat intact.
Butter one side of each slice of bread. Place two slices, buttered side down, on a flat surface. Layer with cheddar cheese, the crab mixture, Mozzarella cheese, and top with the other slice of bread, buttered side up.
Heat a skillet or griddle over medium heat. Cook the sandwiches for 5–10 minutes on each side, pressing slightly with a spatula, until the bread is golden brown, and the cheese is melted.
Slice in half, serve warm, and get ready for that perfect cheesy, crabby crunch in every bite!