Tear the malawach into portions that are approximately two inches in diameter (these don’t have to be circles, but just that approximate size).
Brush each malawach piece with small amount of pesto.
In each malawach piece, place a slice of cheese (approximately a slice that is one inch square) and an olive, and top with another piece of cheese. Add one slice of jalapeño to each at this point, if using. Wrap up malawach to form a ball. Repeat with all malawach pieces.
Heat about one inch of oil in a frying pan over medium-high heat. Your oil is ready for frying if it sizzles when you put a wooden spatula inside. Fry until lightly browned on both sides.