Prepare a breading station: in one shallow dish, whisk together flour, cornstarch (if using), paprika, garlic powder, onion powder, salt, and pepper. In a separate bowl, beat the eggs. In a third dish, whisk together hot sauce and melted butter—the level of heat can be adjusted to taste.
Pound the chicken to an even thickness for uniform cooking. Dredge each piece first in the flour mixture, then dip into the beaten eggs, and finally coat again with the flour mixture. Place on a tray and let rest for 5 minutes to set the crust.
Pour about 1/2 inch of oil into a heavy skillet or heat a high-sided pan over medium-high heat. When the oil shimmers, carefully add the breaded chicken pieces. Fry for 3–4 minutes per side, or until golden brown and cooked through (internal temperature should reach 165°F/74°C). Remove and drain on a rack or paper towels.
If you prefer a lighter option, bake at 425°F (220°C) on a lightly oiled sheet pan for 15–18 minutes, flipping halfway, until crisp and cooked through.
In a small bowl, whisk together the blue cheese sauce base: mayonnaise or sour cream, buttermilk or yogurt, lemon juice, salt, and pepper. Fold in the blue cheese crumbles until slightly chunky. Taste and adjust seasoning; if you like it stronger, add a bit more blue cheese.
Toss the fried chicken in a little extra Buffalo sauce if you want more heat, or brush it lightly for a milder kick.
Toast the brioche buns briefly until lightly golden. Layer the bottom bun with lettuce, then a piece of the spicy fried chicken, and top with a generous spoonful of the blue cheese sauce. Add more lettuce if desired, then crown with the top bun.
Serve immediately with celery sticks and a side of cooling ranch or blue cheese dip. The sandwich shines when the components are warm and the sauce remains creamy and not runny.