Move oven racks to top and bottom position; heat oven to 500°F. Spread potatoes onto a rimmed baking sheet and pour the water onto the baking sheet. Wrap tightly with aluminum foil. Cook potatoes on the bottom rack for 25-30 minutes, until a paring knife or skewer pokes into the potatoes easily through the foil. Carefully remove foil and cool for 10 minutes. If there is any water left on the pan, dry with a paper towel.

Drizzle half (3 tablespoons) of the olive oil over the cooled potatoes and roll them around to coat. Press down on the potatoes to flatten to ⅓ to ½ inch with a second rimmed baking sheet, plate, flat kitchen mallet or the palm of your hand. Sprinkle potatoes with thyme (if using) and season with salt and pepper to taste. Drizzle with the remaining 3 tablespoons of olive oil.

Roast potatoes on the top rack for 15 minutes. Move pan to the bottom rack and continue to roast for 20-30 more minutes, until potatoes are well browned. Serve immediately.