In a pot, bring the cream, shallot, thyme, pepper and butter to a boil. Let reduce by half over medium heat. Strain the mixture through a sieve and return to the pot. Add the trout and cook over medium heat for 3 minutes while stirring.
In a bowl, combine the egg yolks and brandy. While whisking, add a little of the hot cream mixture to temper. Pour the egg yolk mixture into the pot of cream and bring to a boil while whisking.
Divide the rillettes between two ½-cup (125 ml) ramekins and cover with plastic wrap. Refrigerate for 3 hours. Serve with slices of toasted baguette and pickled vegetables, if desired. The rillettes are best enjoyed at room temperature.
Recipes with the "Healthy Pick" stamp have been evaluated by a registered dietitian member of the Ordre professionnel des diététistes du Québec.