Step 1

Grate the onion on the side of a box grater with the largest holes until you have 1/3 cup. Place in a large bowl and reserve the rest of the onion for another use.

Step 2

Shred the potatoes in a food processor fitted with a grating disc with medium-sized holes. Remove and discard any large chunks. Immediately and thoroughly toss with the onion.

Step 3

Line a smaller bowl with cheesecloth and fill with the potato-onion mixture. Twist into a ball and wring out as much of the liquid as possible, reserving the liquid. Let the extracted liquid sit undisturbed for 5 minutes to allow the starch to settle, then pour off the liquid so that only the starch remains.

Step 4

Whisk the egg into the starch and set aside.

Step 5

Add the schmaltz to a cast-iron skillet to measure 1/8 inch deep and heat over medium until shimmering. (Don't let it get over 375 degrees F; that's its smoke point.)

Step 6

Place the potatoes in a large bowl, add the instant mashed potatoes, salt and pepper and combine using your hands. Stir in the egg mixture.

Step 7

Drop a mounded tablespoon's worth of the potato mixture into the skillet and flatten firmly with the back of a spatula. Fry in batches of 4 until browned, flipping only once, 2 to 3 minutes per side, then remove to a rack set over a pan lined with paper towels. Season immediately with additional salt. Continue to add fat in between batches to maintain 1/8-inch depth.