Remove excess moisture: Place the riced cauliflower in the center of a clean kitchen towel or several layers of cheesecloth. Gather the edges and twist firmly over the sink, squeezing out as much liquid as you can. Take your time with this step—the drier the cauliflower, the crisper and more hash-brown-like your patties will be.
Make the mixture: In a large bowl, combine the well-squeezed cauliflower, beaten eggs, shredded sharp cheddar cheese, and kosher salt. Stir with a sturdy spoon or your hands until everything is evenly moistened and holds together when pressed. If the mixture feels too loose to form patties, let it sit 5 minutes so the cauliflower absorbs some of the egg, then stir again.
Form the patties: With slightly damp hands, scoop up about 1/4 cup of the mixture for each patty. Gently press and flatten into thin rounds about 3 inches across and no more than 1/4 inch thick. Thinner patties will give you those extra crispy, lacy edges that mimic classic diner hash browns.
Heat the pan: Set a large heavy skillet (cast iron works wonderfully) over medium heat. Add enough neutral oil or bacon grease to coat the bottom of the pan in a thin, even layer. Let the fat heat until it shimmers; you should hear a gentle sizzle when a bit of the mixture touches the pan.
Fry the patties, first side: Carefully lay several patties into the hot skillet without crowding, leaving a little space between each. Lightly press them with a spatula to keep them flat. Cook without moving them for 4 to 6 minutes, or until the bottoms are deep golden-brown with crisp, lacy edges. Adjust the heat as needed so they brown steadily without scorching.
Fry the patties, second side: Gently flip each patty with a thin spatula. Continue cooking for another 3 to 5 minutes, until the second side is golden and the centers feel set and slightly firm when pressed. Add a touch more oil or grease to the pan between batches if it looks dry; a slightly glossy, lightly greasy surface is what gives that true diner-style crunch.
Drain and season: Transfer the cooked patties to a paper towel–lined plate or a wire rack set over a baking sheet to drain any excess oil. While they’re still hot, taste a small piece and sprinkle with a little extra salt if needed. Keep finished patties warm in a low oven (about 200°F / 95°C) while you fry the remaining batches.
Serve: Serve the cauliflower hash brown patties hot, with the golden-brown, crispy side up. The centers should show bits of white cauliflower when broken open, with the outside crackling like classic shredded hash browns. Enjoy right away for the best texture.
