Season chicken fillets on both sides with salt and pepper.
Melt 20 g (2 tbs) butter in a frying pan over medium heat. Add chicken and cook, turning once, for about 5 minutes, until lightly browned on both sides. Remove from the pan and leave to cool.
Preheat the oven to 190°C. Lightly grease a baking sheet with butter.
Put the remaining butter, the herbs and lemon juice in a food processor or blender, season with salt and pepper and process until smooth. Melt half of the herb butter.
Take one sheet of filo pastry and brush with melted herb butter. Keep the other sheets covered with a damp dish towel. Fold the filo pastry sheet in half and brush again with butter. Place a chicken portion about 2.5 cm from the top end.
Dot the chicken with a quarter of the unmelted herb butter. Fold in the sides of the dough, then roll up to enclose the chicken completely. Place seam side down on a lightly greased baking sheet. Repeat with the other chicken portions.
Brush the filo portions with beaten egg. Cut the last sheet of filo into strips, then scrunch and arrange on top. Brush the parcels with the egg glaze, then sprinkle with Parmesan cheese.
Bake for 35 - 50 minutes, until golden brown.
Serve hot with Brussels sprouts sautéed in hot butter.