In a 3 to 4-quart pot, heat 1 tablespoon of the oil over medium-heat. Add the shallot, mushrooms and carrots. Cook and stir 5 minutes or until tender and fragrant. Remove from the pot to a bowl, and set aside.
Add the remaining tablespoon of oil to the pot. Add the chicken. Season with salt and pepper. Cook and stir 5 minutes or until browned. Stir in the wine, scraping up browned bits from the bottom of the pan. Bring to boiling; reduce the heat. Simmer, uncovered, for 5 minutes. Stir in the shallot mixture, the ¼ cup of cream, and the thyme. Bring to a simmer.
In a small bowl, stir together the flour and butter to make a smooth paste. Stir the flour mixture into the chicken mixture. Cook and stir until thickened and bubbly.
Pour the chicken mixture into a 9-inch deep-dish pie plate. Unroll the pastry sheet onto a work surface. Cut the sheet into irregular pieces. Arrange the pieces over the chicken mixture, overlapping as needed. Brush with additional cream. Bake 20 to 25 minutes, or until the pastry is golden brown. Let stand for 20 minutes before serving.