Shaping, coating, and frying the cakes turned out to be a cinch. The cakes had to be fried in a single batch because any bread crumbs that sloughed off into the oil would burn during the second round. Using a ⅓-cup dry measuring cup, I shaped them into eight 1-inch-thick disks, which would fit snugly in a 12-inch skillet. I pressed the tops and bottoms (the parts that would touch the oil) in panko bread crumbs that I had crushed to a fine consistency to help them stick and then fried the cakes on both sides in ½ cup of hot oil.
The results were mixed: Gloriously crispy crusts formed on the cakes’ exteriors, but their interiors, though not at all gluey, were disappointing flavorwise. With my 1:1 potato-to-fish ratio, the russets had obscured the subtle cod. But when I halved the amount of potato to balance the flavors, there was no longer enough starch to hold the cakes together.
At 3 parts potato to 4 parts fish, the cakes were cohesive, if a bit fragile, but the cod flavor was ideal, so that’s where I landed.