Lay the naan breads on a clean surface. Spread about 2 tablespoons of marinara sauce on each one, leaving a small border around the edges. Top each with a generous amount of shredded mozzarella, halved cherry tomatoes, and sliced olives.
Preheat the air fryer to 375 degrees F for 2 minutes.
Place one or two naan pizzas in the air fryer basket, depending on the size. Make sure they lay flat without folding. Cook for 5 to 6 minutes until the cheese is melted and bubbly and the edges of the naan are golden and crisp.
Remove each naan pizza and immediately top with torn prosciutto, a small handful of fresh baby arugula, and a drizzle of olive oil. The residual heat will slightly wilt the arugula.
Finish with a drizzle of balsamic glaze and a pinch of red pepper flakes. Slice and serve right away. Repeat with the remaining naan pizzas.