Make the Béchamel and Hollandaise sauces and set aside in a warm place.

Heat the water and the red wine vinegar in a medium saucepan to a low simmer. 

Line the work surface with plastic wrap and place the trout fillets side by side atop the plastic wrap. Place another piece of plastic wrap atop the trout fillets. Gently pound the trout with a meat mallet, taking care not to tear the fillets. When the trout is flat gently remove the plastic wrap. Begin on the tail end of the fillet and roll each fillet into a ball. Fasten with toothpicks.

Submerge the trout in the simmering water and vinegar.  Allow the trout to simmer for 9 to 10 minutes until it is cooked through and opaque. Alternatively, fish may be grilled or pan seared.

Make the sauce while the fish is poaching. Melt the butter in a large sauté pan.  Add the shrimp and sauté over high heat for 3 minutes until the shrimp turn pink. Stir frequently to avoid sticking. Add the mushrooms and season to taste with salt and pepper.  Sauté for an additional 2 minutes until the mushrooms are soft. Add the Béchamel sauce to the pan and reduce the heat to low.  Just before you remove the poached trout from the water, remove the shrimp and mushroom mixture from the heat and stir in the Hollandaise sauce. Set the sauce aside.

Remove the trout from the water with a slotted spoon and pat dry with paper towels. Center the poached pieces of trout on 6 plates. Equally divide the sauce atop the poached fish and serve immediately.