Line a baking sheet with parchment paper. Arrange potato slices in a thin, slightly overlapping layer and scatter red onion over the top in an even layer, breaking up some of the wedges into slivers that will caramelize. Drizzle olive oil, season with salt and pepper.
Bake 50-60 minutes, stirring every 10-15 minutes, until potatoes are tender with some crispy edges and onions are soft with some pieces that are caramelized. Transfer to serving platter; sprinkle with thyme leaves and finish with flaky salt if desired. Serve hot.