Preheat your panini grill. Also preheat a toaster oven or oven to 350º F.
Cut off some of the top of a head of garlic. Drizzle the olive oil onto it.
Bake the head of garlic for 20 minutes until golden. (Note it is faster in a toaster oven. If you use a regular oven it may take longer to get the garlic to caramelize.)
Butter one side of four slices of gluten free bread.
On a cutting board, slice roasted red peppers and artichokes.
Place two slices of bread on your panini grill, butter side down on the hot grate.
Spread some caramelized garlic onto each slice of bread. Add two slices of cheese on top of the garlic.
Next, add roasted red pepper and artichoke slices.
Add two more slices of cheese, then put the bread slice on top, butter side facing up towards the heated top grate.
Grill until the cheese is melted.