Peel the potatoes, cut them into chunks and put them in a pot of water to cook. When they are cooked, a fork will easily pierce the potatoes, strain them and mash them into a puree.
Add drained tuna, eggs, onion, garlic, the parsley or basil, salt, pepper to taste and 1/4 cup of breadcrumbs. Mix well with a wooden spoon until all the ingredients are combined. The mixture will be a little wet.
Place the rest of breadcrumbs on a plate.
Form small balls with your hands and then flatten into circular patties. Cover both sides of each with bread crumbs (Alternative method: combine the bread crumbs directly into the mixture by adding a little bit at a time until the entire mixture is consistent. Then make the small balls and flatten into circular patties and place them into a pan with heated olive oil).
Add 1/4 cup olive oil to the pan in order to fry, but not deep fry, the patties. When the oil is heated to frying temperature, add the patties to the pan. Generally, it takes about 3-4 minutes on each side. Be careful not to crowd the pan too much, which will cause the patties to steam rather than fry. They will look golden brown when ready. Remove them from the pan with a slotted spatula and place them on a paper towel to drain extra oil. Change oil when needed.
If you don’t want to fry them, you can spray a baking sheet with olive oil, place the uncooked patties on top, and place them in a pre-heated oven at 350 F (180 C) for 15-20 minutes, flipping the patties halfway through so they can brown on both sides.