Prep the potatoes: Slice the scrubbed potatoes into 1/4-inch-thick rounds or half-moons, keeping the pieces as even as possible so they cook at the same rate. You can peel them if you prefer, but the skins add flavor and texture.
Rinse and dry: Place the sliced potatoes in a bowl of cold water and swish them around to remove excess surface starch, which helps them crisp instead of turning gummy. Drain well, then spread the slices on a clean kitchen towel or paper towels and pat them very dry.
Slice the onion: Cut the onion in half from root to tip, remove the peel, then slice into thin half-moons. Set aside.
Preheat the pan: Set a large, heavy skillet (cast iron works especially well) over medium heat. Add the oil and heat until it shimmers but isn’t smoking.
Start the potatoes: Add the dried potato slices in an even layer. If your pan is crowded, cook in two batches so the potatoes can brown rather than steam. Sprinkle with about 1 teaspoon kosher salt and the black pepper.
Let them brown: Cook the potatoes undisturbed for 4–5 minutes, until the undersides are golden in spots. Flip or stir and continue cooking, turning every few minutes, for another 8–10 minutes, until the potatoes are tender in the center and nicely browned on the edges.
Add the onions: When the potatoes are nearly tender, push them slightly to the sides and add the sliced onion to the center of the pan, along with the butter if using. Toss everything together so the onions are coated in the fat and mingled with the potatoes.
Season and finish: Cook for another 5–7 minutes, stirring occasionally, until the onions are soft and lightly caramelized and the potatoes are fully cooked and crisped to your liking. In the last minute of cooking, stir in the paprika and minced garlic, if using, and adjust salt and pepper to taste.
Serve: Transfer the potatoes and onions to a warm plate or platter. Garnish with chopped fresh herbs, if you like, and serve hot.
Variations & Tips
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