Drizzle 1 teaspoon of the olive oil into a large saute pan and bring over medium heat. Add the onion and celery and stir to coat in the oil. Cook, stirring occasionally, for a few minutes until the vegetables are softened. Stir in the minced garlic and cook for another 30-60 seconds until fragrant. Remove from heat.
In a mixing bowl, combine the eggs (beaten), the vegetable mix from step one, the drained tuna, ¼ cup of the breadcrumbs, ¼ cup of the Parmesan cheese, the mayonnaise, lemon juice, parsley flakes, salt, pepper, and dill. Stir together until well combined.
On a clean surface (I used a cutting mat), scoop out 9 (1/4 cup each) portions of the tuna mixture and flatten/shape them into patties. Combine the remaining ¼ cup of breadcrumbs and 2 tablespoons of Parmesan cheese in a dish and stir together. Sprinkle the crumb mixture over the patties on both sides and press it in to coat.
Wipe out the saute pan from step one to use again. Drizzle 1 tablespoon of oil into the pan and bring over medium heat. When the oil is hot, place half the patties (you’ll have to work in batches depending on the size of your pan, I did 5 the first batch and 4 the second) in the oil and cook for about 3 minutes until golden brown on the bottom. Flip the patties and cook for another 3 minutes or until golden. Transfer the cooked tuna cakes to a cooling rack and repeat with the remaining 2 teaspoons of oil and the remaining patties until all are cooked.