Place salmon fillet on a rimmed baking sheet with parchment paper. Pat the salmon lightly with a paper towel, then season with Kosher salt and black pepper. Dollop with butter, then bake.
While the salmon is cooking, heat olive oil in a small skillet over medium heat. Add shallot and cook until translucent, stirring often. Set aside.
In a large bowl, combine flaked salmon, sautéed shallots, and remaining salmon patty ingredients. Mix lightly until well incorporated, trying not to break the salmon pieces down too much.
Use a large cookie scoop to equally divide the salmon mixture. For salmon fillet, you should get 10 patties. Use your hands to gently press down and form into uniform, round, flat cakes.
Preheat remaining oil and butter in a large nonstick skillet over medium heat. Cook patties at a time until light golden brown on both sides. Transfer to a plate, then repeat with remaining salmon cakes.
Garnish with capers, lemon wedges, marinated or pickled red onions, fresh herbs, micro greens, and of course Greek yogurt sauce!