Put the potatoes into a medium-large saucepan and add enough water to cover them by a couple inches. Bring to a boil and simmer until the potatoes are tender, about 20-25 minutes. Drain them well, then spread out on a baking sheet. Press down on each gently with the back of a fork to flatten each potato.
In a large, heavy skillet, heat a generous drizzle (a few tablespoons) of oil over medium-high heat. Add the garlic and cook until fragrant and lightly brown, about 1 minute. Remove the garlic and discard. Add the potatoes in batches, without crowding the pan, and cook, without stirring, until the bottoms turn golden brown, about 5 minutes. Flip with a thin spatula and cook for another 4-5 minutes, until golden on the other side.
In a small bowl or jar, whisk or shake together the oil, lemon zest and juice, thyme, salt and pepper.
Spoon the dressing over the potatoes and serve.