Make the sauce: Drain and rinse the cashews and place them in a high-speed blender. Add ¼ cup water and the remaining sauce ingredients. Blend on high until smooth and creamy, adding more water if needed to yield a smooth sauce. Set aside.
Make the salmon cakes: Preheat the oven to 400ºF. Place the fish in a baking dish and season with salt and pepper. Roast on the center rack in the oven for 10-15 minutes or until the fish flakes easily when tested with a fork. Remove and let rest until cool enough to handle.
Transfer the salmon to a mixing bowl, discarding any bones or skin. Flake the salmon into small pieces using a fork. Add the mashed sweet potato, cooked quinoa, onion, and eggs to the bowl. Mix until combined. Add the quinoa flakes and a pinch each of salt and pepper. Mix to combine.
In a large skillet over medium heat, heat enough oil to just coat the bottom of the pan. Shape the salmon mixture into 12 patties. Add the patties to the hot skillet, cooking two to three at a time depending on the size of the pan. Cook the salmon patties for 2-3 minutes per side, transferring to a wire rack when done and covering with a piece of foil or parchment paper. Repeat the cooking process with the remaining patties, adding more oil to the pan as needed.
Poach the eggs: Fill a large skillet with at least 1 inch of water. Bring the water to a boil then stir in the vinegar and salt. Reduce heat so that the water comes to a low but rolling boil. Crack the eggs, one at a time, into a small bowl. Carefully drop the eggs into the boiling water and cook for 3 minutes. You can cook two to three at a time. Remove the eggs with a slotted spoon and place on a plate. Repeat until all of the eggs are cooked.
To serve: Place two salmon patties on each plate and top with a bit of arugula. Top the salmon patties with two poached eggs. Spoon some of the cashew sauce on the eggs. Add a sprinkle of salt and pepper and serve.