Fillet your fish and cut the meat into roughly 1/2-inch chunks. In a small pot, bring butter to a slow simmer. Add the fish and gently poach until the chunks are just cooked through, about 5 minutes. Remove fish from the butter and place in the refrigerator to cool. Save butter for searing the fish cakes. As the butter cools, the water will settle at the bottom, making it easy to separate.
Make the aioli. In a blender or food processor, add all of the ingredients and purée until smooth. Place the aioli in the refrigerator to cool and thicken. You can also make aioli from scratch by slowly whisking vegetable or canola oil into egg yolks until it thickens to a mayonnaise consistency. Or, slowly add the oil to egg yolks in a food processor, then purée your flavor ingredients into the aioli base.
Zest the lemon with a microplane before juicing (optional). In a large mixing bowl, add the egg, lemon juice, zest, hot sauce, dijon, 1/4 cup of aioli, parsley, red onion, salt and pepper, and mix until just combined. Now add the fish and bread crumbs and gently combine by hand until the cake mix comes together. Make sure to not completely break the fish pieces apart. The mixture will be a little wet, which is exactly what you want.
Preheat the oven to 400 degrees. Now, form the cakes. Separate the mix into twelve equal portions. Begin by rolling each portion into a meatball shape in your hands. Press the top and bottom to form the hockey puck shape of the fish cake and set aside. Repeat with the remaining portions.
In a large sauté pan or cast iron pan on medium-high heat, add one tablespoon of oil and a spoonful of the poaching butter. Place the cakes in the pan, making sure to leave space in between, and sear for 2-3 minutes or until browned. Flip and repeat. Sear the cakes in batches if needed, then finish cooking them through in the oven for 10 minutes. Serve with the extra aioli. If you feel adventurous, use the leftover butter to make a homemade hollandaise and create a stellar fish cake Benedict.