Mix the filling. Add mashed potatoes, ham, cheese, garlic powder, chives, and 1/2 cup flour to a large bowl. Use your hands to fold everything together until just combined. Do not overmix.
Shape the croquettes. Lightly flour your hands. Divide the mixture into 16 small flat disks, about 1/2 inch thick. Use a cookie scoop to portion evenly before shaping.
Heat the oil. Pour oil into a heavy-bottomed skillet (cast iron recommended) to about 1/4 inch deep. Heat over medium to medium-high heat. Test by sprinkling a few drops of water into the pan. If they sizzle, the oil is ready.
Fry in batches. Add croquettes in a single layer with space between each. Fry, flipping once, until deep golden brown on both sides, about 2 to 4 minutes per side. Do not crowd the pan. Transfer to a paper towel-lined plate.
Rest and serve. Let cool for 5 minutes before serving. Serve with ranch, barbecue ranch, or sriracha mayo for dipping.
Notes
Cooking Tips
Mix with your hands to avoid overworking the potatoes, which can make them gummy.
Use a cookie scoop to portion the mixture before shaping for evenly sized croquettes.
Keep croquettes at about 1/2 inch thick. Thicker patties take longer to cook through.
Do not crowd the pan. Leave space between croquettes so they crisp on all sides.
Fry time varies by stove and pan. Start checking at 2 to 3 minutes per side.
Baked Option: Preheat oven to 450 degrees F. Dip shaped croquettes in egg wash, then in breadcrumbs. Bake on a parchment-lined sheet for about 15 minutes until golden.
Substitutions
Cheese: Cheddar is classic, but swiss, gruyere, or parmesan all work well with ham.
Chives: Green onions are a good substitute.
Ham: Leftover holiday ham, a ham steak, or deli ham all work. Chop into very small pieces.
If They Won't Hold Together
Add flour one tablespoon at a time until the mixture holds its shape when pressed.
Very creamy or thin mashed potatoes need more flour. You can also add one egg to help bind.
Storage and Make-Ahead
Refrigerate leftovers in an airtight container for up to 3 days. Reheat in a skillet for best crispness.
To freeze: arrange shaped (uncooked) croquettes on a baking sheet and freeze for 1 hour. Transfer to a freezer bag and freeze up to 6 months. Fry directly from frozen using the same method, adding 1 to 2 minutes per side.