In a large bowl, combine the mashed potatoes, cheese, garlic powder and 1/2 cup flour. Mix everything together using a wooden spoon.
Lightly flour your hands, then divide the potato mixture into 16 flat discs measuring about half an inch in thickness. TIP: Use a cookie scoop for perfectly uniform portions.
In a large skillet with a thick bottom, heat oil. (I prefer cast iron if it is available). TIP: You can check if the oil has reached a high enough temperature by adding a few drops water to it. If they start to sizzle, the oil is ready.
Flip the croquettes once more, and fry them in batches for about 4 minutes each side, until they are golden. Transfer the croquettes to a paper towel-lined plate. TIP: Don't crowd the pan. Leave enough space between each croquette to crisp them all around.
Allow to cool for 5 minutes before you serve.