Heat remaining 1 tablespoon butter in a large, deep skillet over medium heat. Add chicken; sauté 3 minutes. Add thyme, salt and pepper; sauté 3 minutes or just until chicken is no longer pink (chicken will continue cooking during baking time). Stir in spinach, carrots and currants; sauté just until spinach is wilted, 1-2 minutes. Remove from heat; stir in cheese sauce, mixing well. Transfer mixture to an 11x7-inch baking dish. Sprinkle 1/2 cup cheese over mixture. Place dish on a rimmed baking sheet to catch any juices while baking.
Unfold puff pastry sheet onto a lightly floured surface. Roll out to 11x8-inch rectangle. Place pastry over chicken mixture, turning edges under to fit dish. Bake in a preheated 400°F oven for 16-18 minutes or until pastry is golden brown. Sprinkle remaining 1/2 cup cheese over pastry; let stand 8 minutes or until cheese is melted. Cut pastry into 6 squares with serrated knife. Use a large spoon to dish out each serving.