Place peeled potatoes and garlic in a pot, cover with cold water, and add 1/2 tsp salt.
Bring to a boil, then simmer for 20 minutes until potatoes are knife-tender.
Drain and return the potatoes to the pot to dry out for 20 seconds.
Let potatoes cool and continue to dry.
Sauté onions with butter and a pinch of salt until golden brown.
Mash potatoes and garlic, then mix in cheese, sautéed onions, 1/4 tsp salt, and pepper.
Combine Panko and plain breadcrumbs, seasoning with salt to taste.
Form potato mixture into patties or balls.
Dredge each in flour, dip in egg, and coat with breadcrumb mixture.
Place on a baking sheet and refrigerate to set.
Heat oil to 340-350°F.
Fry croquettes for 1 minute per side or until golden brown.
The recipe yields 8 large or 16 smaller croquettes.