Heat the oil in a frying pan over a medium heat until the pan gets fairly hot.
Sprinkle the cheese on one slice of bread, then spread the other with the pesto. Sandwich together.
Put the sandwich in the pan and use a spatula to put some pressure on it. Grill on one side for around 3-4 minutes, then flip over and repeat until both sides are golden and the cheese has melted. Serve immediately.