Preheat the oven to 400 degrees.
Peel the potatoes and slice off the ends. Cut into 1 inch thick slices. Season both sides of the potatoes generously with salt and pepper.
Heat a cast-iron skillet over medium-high heat. Add the oil and 4 tablespoons of the butter. Sear the potatoes on one side until golden brown, about 5 minutes. Don't touch the potatoes during that 5 minutes! Flip the potatoes and add the broth and minced 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. Spoon the pan sauce all over the potatoes. Season with salt & pepper to taste and garnish with chopped green onions.