Place each pheasant breast between two sheets of cling film and, using a meat mallet or a rolling pin, flatten them to about 1cm/½in thick. Discard the cling film.
Tip the flour, beaten eggs and breadcrumbs into separate shallow dishes. Dredge the pheasant breasts in flour, then egg and finally the breadcrumbs, tossing to coat thoroughly.
Heat a non-stick frying pan over a medium heat. Add a little oil and butter and fry the pheasant breasts on each side until golden-brown and just cooked through (you may need to do this in batches).
Meanwhile, fill a deep-fat fryer with vegetable oil and heat to 180C. (CAUTION: hot oil can be dangerous. Do not leave unattended.)
Add the chips to the fryer and cook for 6-8 minutes, or until golden-brown. Transfer to kitchen paper to drain. Season with salt, to taste, and keep warm until ready to serve.
In a separate frying pan, heat a little oil and butter and fry the eggs until cooked to your liking. Season the eggs with salt and pepper.
To serve, put the pheasant breasts on serving plates and top each one with a fried egg. Place the anchovies and capers on top of the egg and serve the chips alongside.