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Using a cloth or paper towels wrap the grated potato up and squeeze out all of the liquid (potato starch).
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In a large bowl combine grated potato, egg, cornstarch, salt and pepper. Mix until combined.
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Heat a pan (cast iron is best) over medium-high heat, add 1 tablespoon oil and wait for it to heat up.
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Add half of potato mixture to pan and flatten it to make sure it's even all around. Reduce heat to medium.
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Cook for 8-10 minutes (checking at 6 minutes) on one side or until golden brown, and cook 6-8 minutes (adding more oil if necessary) on the other side (to flip rosti over - slide the rosti onto a plate first, then cover it with another plate, flip the two plates and then slide the uncooked side back onto the pan). Repeat with the other rosti.
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For the mushroom sauce heat butter in a pan over medium heat and add diced onion. Cook for a few minutes, remove, and add sliced mushrooms to the pan. Cook mushrooms until starting to brown, add onions back to the pan, reduce heat to low, and add a few dollops of sour cream (to reach desired consistency).
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Serve rosti with mushroom sauce and fresh slivered basil (optional).