Wash, peel and slice potatoes into ¼ inch rounds. Pat the potatoes with paper towels to ensure they are dry. Heat ½ of the duck fat in a wide, high rimmed pan or cast iron skillet set over medium-high heat. Carefully add the potatoes to your skillet and fry for 10 minutes, flipping occasionally to ensure the potatoes are cooking and coloring evenly. Once the potatoes have a nice golden color, turn the heat down to medium and continue to cook until you have reached your 10 minutes.
Next add the other ½ of the duck fat and cover the skillet. Turn the heat to low and cook for 15 minutes. Halfway through cooking, turn the potatoes and add the minced garlic. Be careful not to break the potato slices as you move them. Cover and finish cooking. When cooked, the potatoes should be soft but hold their shape. Using a slotted spoon, transfer the potatoes to a paper towel-lined plate to remove any excess fat. Transfer to your serving dish, season with salt and top with the chopped parsley. Serve immediately.
If your potatoes are very large, you may want to half them lengthwise before slicing into 1/4-inch thick pieces.
I find it helpful to move my skillet to a smaller burner when I am doing the second stage of cooking with the lid on. It helps ensure that the potatoes do not overcook and/or burn.