Preheat panini press/ grill
Carefully slice the panini breads in half, folding out. Spoon 1tbsp Chimichurri sauce on each side of the bread, leaving a 5-10mm gap towards the outer edge.
Place the thinly sliced onion rings on the bottom half of the the bread.
Carefully spoon around 1/3 tin drained tuna (per panini) on top of the onions, maintaining a gap around the outer edges.
Place thin slices of cheddar cheese on top of the tuna.
Fold over the top of the panini, and uses your fingers rub in a little olive oil over the top. Season with freshly ground salt and pepper.
Place in sandwich toaster/grill, close the lid and press down. Cook for 5 minutes or so, or until the top of the panini is firm and first and crispy, and the contents start to ooze out of the sides.
Remove from panini press /grill, slice in half, and serve.