Preheat oil in a deep skillet to 175 C (350 F). The correct temperature ensures crisping without over-absorbing oil.
In a bowl, combine mashed potatoes, cheddar, Parmesan, beaten egg, salt, and pepper. Mix gently to avoid overworking the starch, which causes gumminess.
Portion 30 g (2 tbsp) scoops, flatten slightly and place 5 g (1 tsp) additional cheese in the center, then fold to enclose. You want a sealed seam to keep the molten interior contained.
Roll each puff in flour, then egg wash, then panko breadcrumbs. Notice how the three-layer coating gives a dry, adhesive surface that crisps efficiently.
Fry in batches for 3-4 minutes, turning occasionally, until deep golden brown and an internal temperature reaches about 65 C (150 F). Aromas should be nutty and toasty.
Transfer to a cooling rack for 2 minutes to let the steam escape. This preserves crunch; steam trapped inside will soften the crust.
Serve hot with a tangy dipping sauce. Notice the contrast - the exterior crackles while the center stretches with molten cheese.