Mix the softened butter and minced garlic in a small bowl.
Spread the garlic butter evenly on one side of each bread slice.
Heat olive oil in a skillet over medium heat.
Add shrimp, lemon juice, salt, and pepper; cook until shrimp turn pink and opaque, about 3-4 minutes.
Remove shrimp from heat and set aside.
Preheat a large non-stick skillet or griddle over medium heat.
Place one bread slice garlic butter side down on the skillet.
Add mozzarella cheese generously on the bread.
Top the cheese with cooked shrimp and sprinkle with Parmesan cheese.
Cover with another bread slice, garlic butter side up.
Cook until bottom is golden and crispy, about 3-4 minutes.
Flip the sandwich carefully and cook the other side until golden and cheese is melted, 3-4 minutes more.
Remove sandwich from skillet and let rest for a minute before slicing.
Repeat steps to make remaining sandwiches.
Sprinkle dried parsley over the top for color and flavor.