Cut fillet of trout into four equal portions and reconstruct it on a lightly oiled baking sheet. Set aside.
Pour water and vinegar into a casserole dish. Add shallots and boil down over low heat. Simmer slowly until the mixture has the consistency of marmalade.
Add cream to the reduction and let simmer a few minutes. Finish the sauce by adding knobs of cold butter, whisking until the sauce is smooth.
Season sauce with salt and pepper, then add maple syrup or organic syrup and reheat over low heat. Warm trout in preheated 230°C (450°F) oven for 1 minute. Pour sauce into center of plate and arrange pieces of trout on sauce, in the original shape of the trout.
Surround with diced tomato. Garnish with chervil branch and serve.