Put the butter, rosemary and red pepper flakes in a large microwave-safe bowl. Microwave in 30-second intervals until the butter is melted, about 1 minute. Add the potatoes, 1 1/2 teaspoons salt and a generous amount of pepper and toss together.
Put the potatoes in a 9-by-13-inch metal baking dish in a single layer (a glass baking dish should not be used at this temperature). Bake until the potatoes are a deep golden brown on the bottom, about 15 minutes. Flip and continue to bake until a deep golden brown on the second side, another 15 minutes. Add the chicken broth and garlic and continue to bake until the potatoes are soft and the liquid is almost completely reduced, about 15 minutes more. Transfer the potatoes to a serving platter.
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