Preheat oven to 425°F (220°C).
Cut off ends of russet potatoes, stand potatoes on end, and peel potatoes from top to bottom with a sharp knife to make each potato into a uniform cylinder.
Cut each cylinder in half crosswise to make 6 potato cylinders about 2 inches long.
Place potatoes into a bowl of cold water for about 5 minutes to remove starch from outsides, then pat dry with paper towels.
Place a heavy ovenproof skillet, such as a cast iron skillet, over high heat. Pour in 2 tablespoons of vegetable oil and heat until it shimmers slightly.
Place potato cylinders with best-looking ends into the hot oil, lower heat to medium-high, and pan-fry potatoes until well-browned, 5 to 6 minutes. Season with salt and black pepper.
Flip the potatoes onto the opposite ends. As they cook, use a paper towel held with tongs to carefully blot out the oil from the skillet. Add 3 tablespoons of butter and 4 sprigs of thyme to the skillet.
Pick up a thyme sprig with tongs and use it to paint butter over the top of the potatoes. Cook until butter foams and foam turns from white to a pale tan color. Season with more salt and pepper.
Pour 1/2 cup of chicken stock into the skillet.
Transfer skillet to preheated oven and cook until potatoes are tender and creamy inside, about 30 minutes. If potatoes aren't tender, add 1/4 cup more stock and let cook for 10 more minutes.
Place potatoes on a serving platter and spoon thyme-scented butter remaining in skillet over potatoes. Garnish with thyme sprigs. Let cool for about 5 minutes before serving.