Peel the potatoes and slice off the ends. Cut into 1-inch slices. Season both sides of the potatoes generously with kosher salt and pepper.
Heat a cast-iron skillet (or other heavy-duty, ovenproof skillet) over medium-high heat. Add the oil and 4 tablespoons of the butter. Sear the potatoes on one side until golden brown, about 4 minutes. Flip the potatoes and add the broth, rosemary and garlic. Cut the remaining 6 tablespoons butter into cubes and scatter on top of the potatoes. Transfer the skillet to the oven and cook until fork-tender, about 30 minutes. Garnish with flaky salt and spoon the pan sauce all over the potatoes.