Whisk together egg, onion, lemon juice, thyme, mustard, 3/4 tsp. salt, and 1/4 tsp. pepper in a large mixing bowl. Add salmon and gently stir together. Form into 4 patties, about 3/4 inch thick. (Cakes can be prepared up to 1 day in advance; wrap separately and refrigerate.)
In a nonstick pan, heat oil over medium high heat. Reduce heat to medium low, and lower cakes into pan with a spatula, cooking until browned appx. 5 min. per side. (Because the cakes do not have bread crumbs, they may appear "liquidy" before they enter the pan.) Serve warm with sour cream.