Place potatoes and 1 tablespoon salt in a medium pot and cover with cool water. Bring to a boil over medium-high heat and cook until tender enough to easily pierce with a fork, 15-20 minutes. Remove from the heat, drain and let cool.
In a large mixing bowl, mash the potatoes. Add the tuna, garlic powder, onion powder, black pepper, remaining ½ teaspoon salt, green onion, 3 tablespoons bread crumbs, and 1 egg. Mix well to combine.
Take ⅓ cup of the mixture in the palm of your hand and flatten it. Place about 1 heaping tablespoon of cheese in the center and fold the mixture around the cheese to seal it, forming an oblong croquette.
In a shallow dish, beat remaining egg. On a separate dish spread out remaining 1 cup of breadcrumbs. Run the croquettes, one at a time, through the egg and then coat with breadcrumbs all around. Place them on a pan lined with parchment paper, cover with plastic wrap, and refrigerate for at least 1 hour or up to overnight.
Remove the croquettes from the refrigerator. In a frying pan, heat oil over medium-high heat. Fry the croquettes in batches so as to not overcrowd the pan, turning them occasionally, until golden brown on all sides, 7-9 minutes. Reduce the heat if needed to prevent burning. Transfer to a dish lined with paper towels to drain.
Serve warm.
