In a small mixing bowl, emulsify the softened butter, minced garlic paste, chopped parsley, and a pinch of salt until a uniform compound butter is formed.
Spread a thin, even layer of mayonnaise on the outward-facing side of both bread slices to catalyze the Maillard reaction for superior browning.
Apply the prepared garlic compound butter directly over the mayonnaise layer on both slices.
Preheat a non-stick skillet over medium-low heat to ensure even thermal distribution without scorching the garlic.
Place one slice of bread in the skillet, garlic-butter side down. Immediately top with the mozzarella and sharp cheddar cheese blend.
Position the second slice of bread on top, garlic-butter side facing upwards.
Griddle for 4-5 minutes, or until the base is deep golden brown and the cheese begins to transition to a semi-liquid state.
Carefully flip the sandwich and sprinkle the top browned side with half of the grated parmesan cheese.
Cook the second side for 3-4 minutes, then flip once more briefly to toast the parmesan into a crisp crust for approximately 30 seconds.
Transfer the sandwich to a wire rack for 60 seconds to prevent steam-induced softening before slicing diagonally.