Peel and grate the russet potatoes and sweet onion using the large holes of a box grater. Place the shredded mixture into a clean kitchen towel, twist tightly, and squeeze out all excess liquid over the sink until very dry.

Transfer the dry potato strands to a large bowl. Add the shredded yellow cheddar cheese, beaten eggs, flour, kosher salt, and black pepper. Toss thoroughly until the flour and eggs coat the strands and the cheese is evenly distributed.

Heat the vegetable oil in a cast-iron skillet over medium-high heat until it reaches 350°F (175°C) and begins to shimmer. Drop 1/4 cup mounds of the mixture into the pan, flattening them slightly. Fry for 3-4 minutes per side until golden brown and visibly crunchy.

Transfer the cooked pancakes to a wire cooling rack set over a baking sheet to drain. Plate hot and top each with a thick, smooth dollop of sour cream and a delicate sprinkle of finely chopped fresh chives.