Plug in your panini grill so that it can heat up before putting your sandwich on the grill.
Lightly butter one side of each slice of the gluten free bread. If you want a non-butter option, you can brush the grills with olive oil or avocado oil.
Begin creating your entire sandwich on a plate (NOT on the grills) with the buttered sides of the bread facing outward.
Start with a layer of cheese, then salami, then ham.
Next place the onion and then tomato. Sprinkle a bit of dried oregano on top.
Spread pesto across inside of the remaining piece of bread and then place on top.
Put entire sandwich on the panini maker and pull down the top grill so that the sandwich can heat up.
After about 2 minutes (or the bread is sufficiently toasted), open the grill and remove the sandwich. Slice in half and enjoy while warm!