How to Make It
In a large skillet, heat 1 tablespoon of the oil just until smoking. Season the chicken on both sides with salt and pepper and cook over moderately high heat until browned, about 4 minutes. Turn and sear until just cooked through, 2 to 3 minutes. Transfer to a work surface and cut the chicken across the grain into thin strips.
Heat the remaining 1 tablespoon of oil in the skillet. Add the mushrooms and cook over moderately high heat, stirring occasionally, until tender and browned around the edges, about 7 minutes. Add the shallots and cook, stirring, until tender, about 3 minutes. Add the sherry, sage and thyme and cook, scraping up any browned bits, until the liquid has evaporated. Season the mushrooms with salt and pepper and transfer to a bowl. Add the chicken and Brie and stir until the Brie has melted.
Lay a sheet of phyllo on a work surface with a long edge toward you. Brush the phyllo with melted butter and top with a second phyllo sheet. Cut the sheets in half lengthwise. Spoon 1/4 cup of the filling along the short edge of one phyllo rectangle. Shape the filling into a 6-inch log and roll up one complete turn. Fold in the sides and continue rolling to form a tight cylinder. Fill and roll the second phyllo half. Brush the rolls with butter and transfer to a baking sheet. Repeat with the remaining phyllo and filling. Refrigerate the rolls until chilled.
Preheat the oven to 375°. Bake the phyllo rolls in the upper third of the oven for about 30 minutes, or until golden brown and heated through. Let cool, then transfer to a cutting board. Cut each roll in half and then in half again diagonally. Set the spring rolls upright on a tray and serve immediately.