"A real chicken nugget, at least in the fast food context, is not just a small solid piece of chicken. It's more of a deep-fried, mostly-chicken sausage patty, fabricated from various parts of the bird, such as every legal part. But I like to use chicken thighs."
Place chicken thighs in bowl of a food processor. Add breadcrumbs, kosher salt, paprika, pepper, seafood seasoning, and cayenne pepper. Drizzle in hot sauce and melted butter. Pulse on and off until mixture becomes a coarse paste with very few big chunks, about 18 pulses.
Line a rimmed baking sheet with a silicon mat. Scoop out 24 portions of the chicken mixture with a small ice-cream scoop and place on mat. Cover sheet with plastic wrap. Refrigerate until thoroughly chilled. (Or place pan in freezer for 15 minutes.)
Line a rimmed baking sheet with parchment paper.
Place cornstarch, self-rising flour, and salt into a quart-size zip-top plastic bag. Shake bag to mix thoroughly. Place 3 or 4 scoops of chilled chicken mixture into the bag; shake gently to coat and place on parchment-lined pan. Repeat with the rest of the nuggets. Shape them into flattened ovals, about 5/8-inch thick. Refrigerate pan overnight or until starch on surface is absorbed, flipping over once while they're in the fridge.
Heat oil in a deep-fryer or large saucepan to 300 degrees F (150 degrees C).
Fry nuggets in batches for 1 minute. Drain on a rack over a baking sheet; chill about 1 hour or until you're ready to serve them.
Heat oil in a deep-fryer or large saucepan to 375 degrees F (190 degrees C). Fry the nuggets a second time in batches for 2 minutes. Drain on rack.