Start by making the garlic butter. In a bowl, mix together the melted butter, finely chopped parsley, minced garlic, grated parmesan, black pepper, oregano, and salt until smooth and fully combined. Set aside.
Take your 12 slices of white sandwich bread. For each sandwich, you’ll need one whole slice for the bottom and one criss-cut/hasselback slice for the top. To hasselback the top slice, start by making one vertical cut straight down the center just 2/3 to 3/4 of the way down. Then make one cut halfway between the center and the left edge, and another cut halfway between the center and the right edge—this gives you three evenly spaced vertical cuts. Turn the bread 90 degrees and repeat the same process horizontally. Make sure to slice only about 2/3 to 3/4 of the way down so the bottom of the bread stays intact and you get that perfect grid on top without the slice falling apart.
Grab a nonstick baking tray and lightly brush the surface with some of the garlic butter. Place 6 of the whole bread slices directly on the tray. On each slice, layer one slice of white American cheese and one slice of white cheddar cheese. You can stack them or slightly overlap.
Top each sandwich with one of the hasselbacked slices. Press it down gently so it sits evenly on the cheese. Use a pastry brush or spoon to generously coat the top and all sides of the bread with garlic butter, making sure it gets into every cut and edge.
Bake at 375°F for 10 to 12 minutes, until the cheese is melted and the tops are golden and crisp. For extra browning, broil during the last 1 to 2 minutes—just keep a close eye so it doesn’t burn.
Let cool for a minute, then slice and serve warm.