Preheat the oven to 375°F (190°C). Rinse mussels under cold water, scrub shells, and pull off the beards (pull toward the hinge). Discard any with cracked shells. If a mussel is open, tap it—if it doesn’t close, discard it.
Steam the mussels: Place mussels in a large pot with about 1 cup water. Cover and steam 3–5 minutes, just until the shells open. Discard any that do not open.
Cool 5 minutes until safe to handle. Remove and discard the top shells, keeping the mussel meat on the bottom half shell. Arrange the mussels on a baking sheet.
Make the garlicky béchamel: In a small saucepan over medium heat, melt 2 tablespoons of the butter. Add 2 cloves minced garlic and cook 30 seconds. Whisk in flour and cook 1 minute.
Slowly whisk in milk until smooth. Season with salt and black pepper. Simmer 2–3 minutes, whisking, until slightly thickened. Remove from heat and stir in parsley, lemon juice, and the remaining 2 cloves minced garlic (for extra punch).
Spoon a small amount of béchamel over each mussel. Top with shredded quick-melt/mozzarella and a sprinkle of Parmesan. If using, add a pinch of breadcrumbs for crunch.
Bake 12–15 minutes, until the cheese is bubbling and lightly golden. Optional: Broil 1–2 minutes at the end for deeper browning (watch closely).
Rest 1–2 minutes so the topping sets slightly, then serve hot with extra lemon wedges if desired.