Preheat a grill pan over medium-low heat.
In a medium saucepan over medium heat, add the 3 tablespoons butter, jalapeno and seafood seasoning. Cook until the jalapeno begins to soften, about 3 minutes. Next, add the flour and stir to combine and make a blond roux, about 3 minutes. Add the milk and season with salt and pepper. Stir in the Gruyere and mozzarella and turn the heat to low. Cook for 2 minutes, and then cover to keep warm.
Place the ham on the grill and cook until well marked and warmed, about 2 minutes per side.
Spread 1 tablespoon softened butter on one side of the bread slices and place on the grill, about 2 minutes. Spread the remaining 1 tablespoon softened butter on the other side and flip, cooking about 2 minutes more. Evenly divide the cheese sauce on 4 slices bread and top with 1 slice ham. Place the remaining 4 bread slices on top to create a sandwich.