01 - Set oven to 400°F. Allow to fully preheat while preparing potatoes.
02 - Peel potatoes and cut each into two thick cylinders approximately 2 inches tall. Trim both ends flat for uniform browning.
03 - Thoroughly pat dry potato cylinders with paper towels to remove excess moisture.
04 - Heat vegetable oil in a large ovenproof skillet over medium-high heat. Place potatoes flat side down and cook for 5 to 6 minutes until deeply golden.
05 - Flip potato cylinders with tongs or spatula. Add butter to skillet and let it melt. Spoon melted butter over the tops of the potatoes.
06 - Add smashed garlic cloves, thyme, kosher salt, and black pepper to the skillet. Carefully pour in the broth to avoid splashing hot oil.
07 - Transfer skillet to preheated oven. Roast for 30 to 35 minutes, basting occasionally, until potatoes are tender and most liquid has been absorbed.
08 - Remove from oven, discard thyme sprigs and garlic. Serve immediately, spooning any pan juices over the potatoes.