Preheat the oven: Begin by preheating your oven to 400˚F (200˚C). While it's warming up, line a baking sheet with parchment paper to prevent sticking.
Prepare the salmon: Place the salmon filet, skin side down, on the prepared baking sheet. Drizzle it with 1 tablespoon of olive oil, then sprinkle with ½ teaspoon kosher salt and ¼ teaspoon pepper. Bake in the oven for 15-20 minutes or until the salmon is flaky and reaches an internal temperature of 145°F (63°C). Remove from the oven and let it cool before flaking into a medium bowl, discarding the skin and bones.
Mix the ingredients: To the bowl of flaked salmon, add 2 large room-temperature eggs, 1 teaspoon minced garlic, ¼ cup chopped yellow onion, ½ cup dry bread crumbs, 1 teaspoon Old Bay seasoning, and another ½ teaspoon of kosher salt. Mix the ingredients thoroughly until well combined.
Form the patties: Shape the mixture into 8 patties, approximately 2 inches wide and ½ inch thick.
Cook the patties: Heat 1 tablespoon of olive oil in a skillet over medium heat. Place the patties into the skillet in batches (depending on size) and cook each side for about 3-5 minutes or until they are golden brown. Use a spatula to carefully flip them to avoid breaking.
Drain and serve: Once cooked, drain the patties on paper towels. Serve the salmon patties warm, garnished with lemon wedges and paired with tartar sauce for dipping.