Arrange a rack in the middle of the oven and heat the oven to 450°F. Stir together 2 tablespoons melted unsalted butter, 2 tablespoons olive oil, 1 teaspoon kosher salt, and ½ teaspoon black pepper in a small bowl.
Peel 2 pounds Yukon gold or russet potatoes, if desired. Trim the rounded ends slightly, then cut the potatoes crosswise into 1-inch thick rounds.
Add the potatoes and 1 tablespoon chopped rosemary to the butter mixture and toss well to coat.
Transfer the potatoes cut-side up to a rimmed 9x13-inch metal baking pan (avoid glass as it could shatter) or baking sheet (quarter sheet pan) and arrange in a single layer.
Drizzle any remaining butter mixture over the potatoes.
Roast until the potatoes easily release from the pan with tongs and the bottoms are beginning to turn golden brown, about 15 minutes. Flip the rounds and roast until the bottoms and tops are deep golden brown, about 15 minutes more. Remove the pan from the oven.
Carefully pour 1 cup low-sodium vegetable or chicken broth into the pan and add 4 peeled and smashed garlic cloves. Roast until the potatoes are very tender and most of the broth is absorbed, about 15 minutes.
Roast until the potatoes are very tender and most of the broth is absorbed, about 15 minutes.
