Add the garlic and 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 the
skillet.
Heat 2 tablespoons oil in the skillet over medium heat
until shimmering. Add half of the potatoes and press into
the bottom of the pan with a rubber spatula. Season with
salt and pepper. Spread the onion/mushroom mixture
evenly over the potatoes and top with the remaining
potatoes. Press down into an even disk, using the spatula.
Season with salt and pepper. Cook, swirling and shaking
the pan occasionally, until the potatoes are deep golden
brown and crisp on the first side, about 7 minutes.
Carefully slide the rösti onto a large plate. Set another
plate on top of it, upside down, grip the edges, and invert
the whole thing so the rösti is now cooked side up.
- Heat the remaining 2 tablespoons oil in the skillet and
slide the rösti back in. Season with salt and pepper.
Continue cooking, swirling and shaking the pan
occasionally, until the rösti is deep golden brown and
crisp on the second side, about 7 minutes longer. Slide
the rösti into a cutting board. Serve immediately, with
aioli or mayonnaise, or ketchup.