In a large bowl, combine the thinly sliced potatoes, onions, and chopped garlic. Season with salt and pepper to taste, tossing well to coat the vegetables thoroughly.
Sprinkle the flour over the potato mixture, tossing again to ensure that the potatoes and onions are evenly coated.
Warm a cast-iron skillet over medium-high heat. Add the butter and melt, then add the coated potatoes and onions to the skillet.
Cook the potatoes for 10 minutes, carefully flipping them over frequently to prevent burning.
After 10 minutes, pour the chicken broth into the skillet. Cover the skillet with a lid and continue cooking for another 10 minutes, or until the potatoes are tender.
Serve the Southern smothered potatoes warm, as a delightful side dish or a comforting main course.