Preheat the oven to 400°F (205°C) and line a baking sheet with parchment paper.
Heat 1 teaspoon extra virgin olive oil in a small saucepan over medium heat. Add the minced green onions and sauté for 3–4 minutes until softened; remove from heat and let cool slightly.
In a medium mixing bowl, whisk the 2 eggs. Add 1/2 cup panko breadcrumbs, 2 tablespoons mayonnaise, 1 teaspoon seasoned salt, 1 teaspoon minced garlic, the cooled green onion mixture, and the zest and juice of 1 medium lemon; stir until combined.
Fold in the 10 ounces flaked albacore tuna gently until just combined, being careful not to overmix.
Scoop the mixture onto the prepared baking sheet and shape into patties. For thin crispy patties, make 6 patties using about 1/3 cup each. For thicker patties, make 3 patties using about 2/3 cup each.
Bake thin patties for 10 minutes, flip, then bake an additional 6–8 minutes until browned and crispy. For thicker patties, bake 12 minutes, flip, then bake another 8–10 minutes until browned and crispy.
Allow patties to cool for about 5 minutes before serving.