Spread 3 tablespoons butter on 1 side of all the bread slices. Toast bread, butter side down, in a large skillet until golden brown, about 2 minutes and then remove.
In a small bowl, mix together mayonnaise, parmesan cheese and remaining 3 tablespoons butter.
In another bowl, combine the shredded cheddar, shredded Monterey Jack and shredded Gruyere.
To assemble sandwiches:
Top the toasted side of 4 bread slices with sliced Brie and sprinkle the cheese mixture evenly over the Brie. Top with remaining bread slices, toasted side facing inward. Spread mayonnaise mixture on the outsides of each sandwich. Place in same skillet, over medium low heat and cook until golden brown and cheese is melted, 5-6 minutes on each side. Serve immediately with ALL THE KETCHUP.
Notes
Seriously, even if you aren't taking it next level and adding cheese on the outside, definitely switch from butter to mayo every single time you grill a sandwich.