3Russet potatoes (about 1 pound) rinsed and cut into 1/16th-inch matchsticks by hand or with a mandolin
1tablespoonextra-virgin olive oil
Sour creamfor garnish
Sauté The Mushrooms: Heat 1 tablespoon of the oil in a large well seasoned cast iron or nonstick skillet over medium-high heat. When the oil shimmers, add the mushrooms, season with salt and pepper and add half of the thyme. Cook, stirring occasionally, until mushrooms are golden brown, about 10 minutes. Discard the thyme stems and set mushrooms aside.
Cook The Onions: When the mushrooms are ready, remove from heat and set aside. Return the pan to the stove, add 1 tablespoon of the butter and place over medium-high heat. When it foams, add onions and cook, stirring occasionally, until softened, about 5 minutes. Add garlic and remaining thyme and cook, stirring frequently, until fragrant, about 30 seconds. Season to taste with salt and pepper. Transfer to a small bowl and wipe out skillet. Discard the thyme stems and set onions aside.
Microwave The Potatoes: Meanwhile, spread the matchstick potatoes on a large microwave-safe plate and microwave on high heat until hot all the way through and softened but still slightly crunchy, about 5 minutes.
Cook The Rösti: Heat 1 tablespoon each oil and butter in the pan over medium heat until shimmering. Add half of potatoes and press into bottom of the pan with a rubber spatula. Season with salt and pepper. Spread onion mixture evenly over the potatoes and top with remaining potatoes. Press down into an even disk shape using a rubber spatula. Season top with salt and pepper.
Cook, swirling and shaking pan occasionally until deep golden brown and crisp on the first side, about 10 minutes. Carefully place a large cutting board of the pan, grip the sides (with some kitchen towels) and, carefully flip the pan so the rösti is now cooked-side up on the board.
Heat remaining oil and butter in the skillet and slide rösti back in the pan. Continue cooking, swirling and shaking pan occasionally until deep golden brown and crisp on the second side, about 8 minutes longer. Slide rösti to a cutting board. Serve immediately with sour cream and mushrooms.