By An Edible Mosaic
Add the butter to a medium skillet over medium-low heat. Once melted, add the onion. Cook until deep golden brown, about 10 to 15 minutes, stirring occasionally. Cool slightly.
Add the grated potato and salt to a large bowl. Add enough cold water to cover by 3 inches. Mix it briefly to help disperse the salt. Soak for 30 minutes.
Drain the potatoes well in a fine mesh sieve, pressing with a spoon to get out as much water as possible.
Add the well-drained potato to the bowl with the potato starch in the bottom, along with the egg, flour, and baking powder. Stir to combine. Mix in the caramelized onion.
Add the duck fat to a medium-large skillet over medium-high heat. Once hot (around 365 to 375F), add 3 tablespoons of the potato mixture per latke. Try to drain off any excess liquid before adding the potato mixture to the skillet.
Fry the latkes until golden on both sides, about 4 minutes total, flipping once halfway through.
Transfer the fried latkes to a paper towel-lined plate to drain off any excess oil.