Prepare onion rings per package instructions.
Brush one side of each slice of bread with melted butter.
Place 1 slice bread, butter side down, on working surface and layer fontina, onion rings, arugula and gruyere. Top with remaining slice of bread (butter side out).
Preheat skillet to medium heat.
Place sandwich in heated skillet (weight it down if possible) and cook until browned and cheese is melting (3-4 min). Flip sandwich over and brown other side.
Serve with remainingl Alexia onion rings.