Preheat the oven to 180C/350F/Gas 4. Season the skin of the chicken with salt and pepper.
Heat a large frying pan over a medium-high heat. Add the butter and sunflower oil. When the butter is foaming, add the chicken, skin-side down, and cook for five minutes, until golden-brown and crisp. Remove from the pan and leave to one side.
Cut each piece of cucumber to the same length as one of the chicken breasts, then slice into 3mm/1/8 in thick strips.
Remove the frying pan from the heat then wipe clean with kitchen paper. Return to the heat, add the olive oil and cucumber, season with salt and pepper and cook for 4-5 minutes, tossing continuously, until the cucumber is translucent but still retaining its crunch. Add the paprika and stir, then drain on kitchen paper.
Lay four 30cm/12in square sheets of baking paper on a work surface. Put one-quarter of the cucumber on one of the sheets, laying it out lengthways in the centre. Put a chicken breast on top and fold in the sides and the bottom of the paper so the top is open.
Pour three tablespoons of cream on top, then fold the paper over and tightly fold the top to seal and make a parcel. Repeat to make four parcels.
Transfer to a baking tray and roast for 8-10 minutes. Turn off the oven and open the door so it's ajar. Leave the chicken for two minutes until cool enough to handle.
Carefully open one end of each parcel and pour the juices into a small sauté pan. Close the parcels again and return them to the oven.
Put the sauté pan over a medium heat and bring to the boil, then turn the heat to low and simmer for five minutes, until reduced in volume by half.
Meanwhile, whip the remaining cream until soft peaks form.
Remove the pan from the heat and whisk in the whipped cream. Return to the heat and bring to a simmer, then immediately remove from the heat. Stir in the parsley and season with salt and pepper.
To serve, slide the parcels onto plates and open the tops. Spoon the sauce over the chicken and sprinkle with the almonds before serving.