Prep the chicken dredge by adding the flour to a wide-rimmed baking dish. To another dish, toss the bread crumbs with the salt and ground paprika. To a medium dish, beat the 3 large eggs together. This will give you a good assembly line.
Preheat the oven to 350 degrees F. To a clean baking sheet, brush the surface with the oil and transfer to the oven. (The oil will get really hot while you assemble the rest of the ingredients.)
Using tongs, dip chicken, piece by piece, first in the flour, then the egg and, lastly, the bread crumbs. Feel free to sprinkle the tops and the sides of the chicken with the bread crumbs. I found it easier to do it this way. Transfer to a plate and repeat with the remaining pieces of chicken.
Place the chicken on the hot baking sheet in the oven and bake on the first side for 15 minutes. Flip and cook on the opposite side for another 20 minutes.
While the chicken is cooking, let’s make the hot sauce. In a small saucepan, melt the butter. Skim the fat solids offthe top and discard. This will leave you with clarified butter. Add the cayenne pepper, sugar, garlic powder, paprika and salt. Warm until the sugar and salt are dissolved.
When the chicken is done cooking, transfer the pieces to the brioche buns. I added about 1 to 2 pieces to each of the bottom of the buns.
Brush the tops liberally with the spice/butter mixture. I found that what I really wanted was the paste that sits at the bottom; scoop that stuff out and brush that on. The more the better! Top with a bit of cole slaw, if desired, and add the other half of the brioche bun to the top. Add a bread and butter pickle to the top and poke a skewer through the center so it holds its shape! Serve immediately.