Preheat oven to 350.
Place salmon skin side down the baking sheet. Drizzle olive oil on the filet. Bake for 20 minutes. Remove from oven and let rest for 2 minutes. Using two forks separate salmon flesh from skin.
Place the garlic, egg yolks, mustard, vinegar and lemon juice in a food processor and process until combined.
With the motor running, slowly pour in the oil in a thin stream and process until the aioli is thick and creamy, add extra olive oil if needed.
Bring 2 cups of water to a boil and cook sweet potatoes until fork tender.
Drain potato and let cool. In a larger bowl mash the potatoes. Add the salmon, eggs, 2 tbsp aioli, and juice from half a lemon Mix until well combined. Don’t be afraid to use your hands. Form mixture into 2 inch patties.
Heat a thin layer of oil in 10-inch nonstick skillet. Fry each pattie over medium heat for approximately 5 minutes per side, until golden on both sides. Add more oil to skillet if necessary.