Melt the unsalted butter in a small saucepan over medium heat and add the minced garlic, sautéing for about 1-2 minutes until fragrant. Remove from heat and set aside.
In a mixing bowl, combine the shrimp, cream cheese, salt, and pepper, ensuring the shrimp are evenly coated.
Heat half of the garlic butter in a skillet over medium-high heat, add the shrimp, and cook for about 3-4 minutes until the shrimp are pink and opaque. Remove from heat and set aside.
Preheat your skillet or griddle over medium heat and brush one side of each slice of bread with the remaining garlic butter.
Assemble the sandwich by placing one slice of bread, buttered side down, in the skillet. Layer mozzarella cheese, cooked shrimp, more mozzarella, and another slice of bread, buttered side up.
Cook the sandwich for about 3-4 minutes until the bottom is golden brown and the cheese starts to melt. Carefully flip the sandwich and cook for another 3-4 minutes until golden brown and the cheese is fully melted.
Remove the sandwich from the skillet, allow it to rest for a minute, then slice it in half.
Optionally, sprinkle with chopped parsley for garnish before serving hot.