Preheat your oven to 200°C / 390°F (or 180°C if using a fan-forced setting).
Prepare the Potatoes: Slice each potato into cylinders approximately 6 cm (2 inches) in diameter and 7 cm in height. Cut these in half horizontally to form eight smaller cylinders, each around 3.5 cm (1.4 inches) tall. Follow one of the cutting methods described below.
Season the Potatoes: Pat the potatoes dry thoroughly. In a large bowl, toss them with half of the olive oil, salt, and pepper, ensuring they are well-coated.
Sear the Potatoes: In a heavy-based, oven-safe skillet, heat the remaining tablespoon of olive oil over medium-high heat. Place the potato cylinders flat side down in the skillet. Sear each side for about 6-8 minutes, or until they develop a golden crust.
Add Flavor and Cook: Add the butter and thyme to the skillet. As the butter melts, use a spoon to baste the potatoes continuously with the buttery mixture. Pour in the stock and bring it to a boil. Carefully transfer the skillet to the oven and bake for 30 minutes. Halfway through, around the 15-minute mark, baste the potatoes again. The stock will gradually be absorbed, leaving a rich, buttery coating.
Final Baste and Serve: Once the potatoes are tender, remove them from the oven and give them one last baste. Serve immediately for a gourmet touch—pair with a juicy steak, béarnaise sauce, and a side of buttered peas for an elevated meal experience.