Boil potatoes until fork-tender, about 15 minutes.
Drain potatoes and mash until completely smooth.
Mix in cheddar and mozzarella cheese while warm.
Add one egg, flour, salt, pepper, garlic powder.
Refrigerate mixture for 30 minutes until firm.
Shape mixture into finger-sized sticks carefully.
Beat remaining egg in shallow bowl.
Dip each stick in beaten egg first.
Roll sticks in panko breadcrumbs evenly.
Heat oil to 350°F in deep fryer.
Fry sticks for 3-4 minutes until golden.
Remove with slotted spoon onto paper towels.