In a small pan, sauté onions in a little olive oil over medium heat. Cook 5-7 minutes, stirring occasionally, until onions are softened and translucent. Remove from heat and set aside.
Thoroughly drain the cans of salmon (reserving the liquid) and place the drained salmon in a large mixing bowl. Pick through the salmon and remove any skin and bones.
Gently break up the salmon, then add the sautéed onion, crushed saltine crackers, parsley flakes, salt, garlic powder, paprika, black pepper, cayenne pepper, lemon juice, mayonnaise and eggs to the bowl. Gently stir to combine ingredients (don’t overmix), then cover bowl with plastic wrap and refrigerate for at least 20 minutes. Note: If your mixture seems too dry to shape into burgers, add a little of the reserved salmon liquid and stir in before refrigerating. If you don’t have this problem, you can discard the liquid.
Once chilled, shape the mixture into 8-10 patties. Size will be smaller and flatter than a regular burger.
Heat a little olive oil on a griddle set to 300°F (or a large skillet over med-low heat) and add salmon patties. Leave room in between patties for flipping. Cook for 5-10 minutes per side until browned. Patties should flip easily. If patty is difficult to flip, let it cook a little longer until it easily releases. Otherwise, it may break while flipping.
To serve, place cooked patty on a hamburger bun along with desired toppings. Or, serve along with grits and eggs for breakfast. Enjoy!