In a mixing bowl, thoroughly blend the softened butter with olive oil, minced garlic, parsley, Parmesan cheese, and a light touch of salt until the mixture is cohesive and spreadable.
Evenly coat one side of each bread slice with the prepared garlic butter spread.
Warm a skillet over medium heat. Lay two slices of the prepared bread, buttered sides down, into the pan.
Top each with two slices of cheese.
Cover with the remaining bread slices, positioning them buttered sides facing up.
Toast the sandwiches until the bottom is golden brown and crisp, approximately 3 to 4 minutes.
Flip gently and continue to cook the other side for another 3 to 4 minutes, or until the exterior is deeply golden and the cheese has melted completely.
Slice the sandwiches in half and serve immediately while warm and melty.