Cut the chicken breasts in half horizontally nearly all the way through, then open each one out into a heart shape.
Lay a large sheet of cling film onto a work surface, place one butterflied chicken breast on top, then cover with a second sheet of cling film. Gently flatten the chicken breast with a meat mallet or rolling pin to a thickness of 1cm/½in. Discard the cling film.
Repeat the process with the remaining chicken breasts.
Place 2 pieces of emmental onto one side of each flattened chicken breast. Fold over one slice of ham and place it on top of the cheese. Fold the other half of the chicken over the filling and press down lightly. Repeat the process with the remaining chicken breasts.
Sprinkle the flour onto a plate and season with salt and freshly ground black pepper. Beat the eggs in a bowl. Sprinkle the breadcrumbs onto a separate plate.
Dredge each filled chicken breast first in the flour, then dip it in the beaten egg, then roll it in the breadcrumbs to cover.
Heat 125g/4½ oz of the butter in a large frying pan over a medium heat. When the butter is foaming, add the chicken breasts (in batches if necessary) and fry for 4-5 minutes on one side, or until the breadcrumbs are golden-brown. Turn the chicken breasts over and fry for a further 4-5 minutes, basting the chicken with the butter in the pan at intervals. Try to keep the heat low enough to avoid burning the breadcrumbs or butter, but high enough to cook the chicken completely, until no trace of pink remains.
When the chicken breasts are cooked through, the coating is golden-brown and the cheese filling has melted, remove the chicken breasts from the pan and set aside on a warm plate.
Bring a pan of salted water to the boil, add the beans and cook for 3-4 minutes, or until just tender. Drain well.
Return the pan to the heat, add the remaining butter, then fry the flaked almonds for a few seconds until toasted. Return the beans to the pan, mix well, then season, to taste, with salt and freshly ground black pepper.
Serve the chicken cordon bleu on serving plates with a spoonful of beans alongside.