Rinse the mussels under cold water and soak for 15-20 minutes to remove sand. In a large pot, add water and bring to a boil. Place mussels in and cook until shells open, about 5-7 minutes. Let cool, then remove one half of each shell.

In a medium saucepan over medium heat, melt butter until bubbly. Add minced garlic and sauté until fragrant, about 1 minute. Stir in breadcrumbs and cook for another minute. Gradually pour in milk while whisking, cooking until the mixture thickens, about 3-5 minutes. Season with salt before removing from heat.

Preheat the oven to 355°F (180°C). Arrange cleaned mussel halves on a baking tray. Spoon the bechamel mixture into each mussel half and sprinkle quick-melt cheese on top.

Place the tray in the oven and bake for 10-15 minutes until the cheese is melted and golden. Let cool slightly before serving.