Peel and mash the potatoes and set aside.
Rinse capers under running water and dry with kitchen paper. Set aside.
Put the tuna in a bowl with the capers and shelled eggs. Reduce to a cream with an immersion blender or in a blender.
Add the tuna to the potatoes. Also, combine Parmigiano, bread crumbs, salt, and a tablespoon of olive oil.
Knead with your hands until the mixture is smooth and firm—not too soft or hard. If it seems too firm, add a few tablespoons of milk and knead again; however, if it looks too soft, add mashed potatoes or breadcrumbs.
Using a sheet of baking paper, help shape the mixture into a meatloaf, wrap it in the paper, and then seal the package in aluminum foil.