Preheat the oven to 400 degrees F.
Peel the potatoes and slice off the ends.
Cut into 1-inch slices.
Season both sides of the potatoes with kosher salt and pepper.
Heat a cast-iron skillet over medium-high heat.
Add 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 by grating the cheese and spoon the pan sauce all over the potatoes.