Preheat the oven to 425°F (220°C). Rub the salmon with 1 tablespoon olive oil and place on a baking sheet.
Bake the salmon for about 10 minutes, until just undercooked in the center; remove and let cool slightly.
Flake the cooled salmon into large pieces and transfer to a mixing bowl, including any juices on the tray.
Add the cooked quinoa, sliced green onions, chopped dill, Greek yogurt, egg, lemon juice, Dijon mustard, kosher salt, and black pepper to the bowl.
Mash and mix everything together with a fork or potato masher until the mixture holds together but still has texture.
Form the mixture into 10 even patties and place them on the baking sheet lined with parchment or lightly oiled.
Reduce the oven temperature to 350°F (175°C) and bake the patties for 8 to 10 minutes, until cooked through and lightly golden.