First make the shrimp mousse. Bring a wide, shallow pan of water about an inch deep to a simmer. Add the shrimp and poach just until they turn pink. Remove, drain, and allow to cool to lukewarm.
In a food processor, combine eggs, salt, pepper, dry mustard and garlic. Run the processor on and off a few times to chop and blend everything. Add the shrimp and turn the processor on. Add the cream while the machine is running and process into a paste. Add a little water from the poaching pan if necessary to keep it rather light. Don't overdo the blending of these ingredients. Small lumps are okay.
Add the lemon slices, white wine, parsley stems, and peppercorns to the poaching pan, and return to a simmer. Add the trout and poach for six to eight minutes, depending on thickness, until the flesh is opaque. Remove and drain.
Cut the trout fillets across and lengthwise into two thin halves. Place one half of the trout over the bottom half of the puff pastry. Spoon about 2 Tbs. shrimp mousse over the trout. Top with the other half of the fish.
Brush edges of puff pastry dough with beaten egg, then fold top half over and press in place to form an envelope around the trout. If you really want to get fancy, cut the pastry envelope in the shape of a fish. You can stick the parts of the dough you cut off back onto the fish to create fins. Make scale-like indentations on the side with the tip of a spoon.
Place the pastry on a lightly oiled baking sheet. Put it in a preheated 375-degree oven for eight to ten minutes--until the pastry has puffed and has just turned brown. Push the tines of a kitchen fork into the thickest of the fish and hold it there for about five seconds. Carefully touch the tips of the fork to your lips; if it feels warm, the fish is done. Serve immediately.
