Combine all prepped trout cake ingredients in a large bowl. Mix with hands until they start to hold their shape. If too wet, add 1/8 cup more breadcrumbs at a time.
Weigh 3 oz portions out with a scale, using your hands to pat them into a cake shape as you go. Let sit on a lined baking sheet in the fridge while you make the aioli.
To make the aioli, combine ingredients into a small bowl.
When ready to cook the cakes, sear in butter until both sides are golden-brown and the center is warm. Serve with chive aioli.