Cover phyllo stack with overlapping sheets of plastic wrap and then a damp kitchen towel.
Melt 4 tablespoons butter. Arrange 1 phyllo sheet on a work surface and brush with some melted butter. Arrange another sheet to overlap the first and form a 17-inch square and brush with butter. Continue layering with remaining 6 sheets and butter. Drape phyllo stack over a 10-inch (25cm) tart pan with a removable bottom and fit phyllo into pan. Crumple overhang against inside edge of rim to create a ragged edge that stands about 1 inch above rim. Chill shell, loosely covered, until firm, at least 3 hours.
Preheat oven to 190 degrees C (375°F).
Prick bottom of shell all over with a fork and bake in middle of oven until golden, about 15 minutes. Cool shell in pan on a rack. Shell may be made 1 day ahead and kept, covered, at cool room temperature.
In a saucepan melt remaining 1 1/2 tablespoons butter over moderately low heat and whisk in flour. Cook roux, stirring, 3 minutes then whisk in milk and cream. Bring mixture to a boil, whisking constantly, and simmer, whisking occasionally, 3 minutes. Season mixture with salt and pepper and cool.
Discard skin and bones from trout and break fish into small pieces. Separate eggs. In a food processor pulse together milk mixture, trout, yolks, horseradish and dill until smooth then transfer to a large bowl.
In another large bowl with an electric mixer beat whites with a pinch salt until they just hold stiff peaks. Stir one fourth whites into trout mixture to lighten and fold in remaining whites gently but thoroughly.
Pour soufflé mixture into shell and run tip of a knife around edge of soufflé to aid rising. Bake soufflé on a baking sheet in lower third of oven until puffed and golden brown, about 25 minutes. Serve soufflé immediately.