In a large pot place the 2 potatoes, skin on, and cover with water. Place over high heat and boil until pierced with the knife you feel no resistance and the potatoes are done. Remove, drain and when ready to handle, remove the skin and place the potatoes thru a ricer and place into a bowl.
Add the tuna, olive oil, cheese, parsley, eggs, salt to taste, and mix well. Add a handful of the breadcrumbs at the time and incorporate well until you will be able to work it with your hands easily.
In a plate or bowl add breadcrumbs. With an ice cream scooper grab some of the potatoes mixtures and drop in your hands and form a perfect ball. Roll in the breadcrumbs and set aside until all the potatoes tuna mixture is done.
In a large skillet over high heat warm the frying oil. Fry the croquettes moving them to evenly fry them.
On a cutting board, place paper towels to cover the wood, add a cooling rack over it and once the croquettes are done place them over the cookie sheet.
Preheat oven at 375F. Cover the bottom of a cookie sheet with parchment paper and place the croquettes. Slightly flatten them to better cook.
Sprinkle some olive oil over them and bake for 30 minutes, turning them once halfway thru.