Marinate the Chicken: In a bowl, combine the olive oil, minced garlic, lemon juice, dried herbs, salt, and pepper. Introduce the chicken breasts to the marinade, ensuring they are thoroughly coated. Cover the bowl and place it in the refrigerator for a minimum of 30 minutes to let the flavors penetrate.

Cook the Chicken: Preheat a grill or grill pan over medium-high heat. Grill the chicken breasts for 5-7 minutes per side, or until the internal temperature reaches 165°F (74°C).

Caramelize the Onions: While the chicken is grilling, heat a small amount of oil in a skillet over medium heat. Add the sliced onions and cook, stirring occasionally, until they are soft and golden brown, about 10-15 minutes. Remove from heat and set aside.

Prepare the Honey-Dijon Spread: In a small bowl, mix together the mayonnaise, Dijon mustard, and honey.

Assemble the Sandwiches: Place a handful of shredded sharp cheddar, mozzarella, and Gruyère cheese on the bottom slice of each sandwich. Top with the sliced grilled chicken, caramelized onions, tomato slices, and arugula. Add another handful of cheese on top before placing the remaining bread slices, honey-Dijon side down, to close the sandwiches.

Grill the Sandwiches: Heat a large skillet or grill pan over medium heat. Lightly butter the outside of each sandwich. Place the sandwiches in the skillet and cook for 3-4 minutes per side, pressing down gently with a spatula, until the bread is golden and crispy and the cheese is melted and gooey.

Serve: Slice the sandwiches in half and serve immediately while the cheese is still melty and delicious. Enjoy your Grilled Chicken Three-Cheese Sandwich with a side of chips, a light salad, or a bowl of soup.