Slice each chicken breast horizontally into two fillets to make four pieces.
In a shallow bowl, whisk together the plain flour, cornflour, paprika, garlic powder, onion powder, cayenne pepper (if using), salt and black pepper.
In another shallow bowl, whisk the large eggs with the full-fat milk.
Coat each chicken fillet in the flour mix, dip into the egg wash, then coat again in the flour mix. Set aside.
Heat the vegetable oil in a heavy-based pan or Dutch oven over a medium-high heat until it reaches about 180 °C.
Fry two chicken fillets at a time for 5–7 minutes on each side, until golden and cooked through. Drain on a wire rack and repeat with the remaining fillets.
Meanwhile, peel and chop the floury potatoes into roughly 2.5 cm pieces. Place in a pan, cover with cold water, add a pinch of salt and bring to the boil. Simmer for 15–20 minutes until tender, then drain.
Return the potatoes to the pan. Add the unsalted butter and full-fat milk, then mash until smooth. Season with salt and black pepper.
For the gravy, melt the unsalted butter in a saucepan over a medium heat. Stir in the plain flour and cook for 1–2 minutes to form a roux.
Gradually whisk in the chicken stock and simmer for 5–7 minutes, stirring, until the gravy thickens. Season with salt and black pepper.
If you like, lightly toast the brioche buns. Place a fried chicken fillet on the bottom half of each bun.
Top each with a spoonful of mash and a good drizzle of gravy. Sandwich with the top halves and serve straight away.