Melt 2 tablespoons of the butter in a medium saucepan over medium heat. Add flour; cook 1 minute, whisking constantly. Stir in milk or stock; bring to a simmer, whisking frequently. Simmer until sauce thickens, 2-3 minutes. Stir in sherry; simmer 2 minutes. Remove from heat; stir in 1 cup of the cheese until cheese melts.
Heat remaining 1 tablespoon butter in a large, deep skillet over medium heat. Add chicken; saut 3 minutes. Add thyme, salt and pepper; saut 3 minutes or just until chicken is no longer pink (chicken will continue cooking during baking time). Stir in spinach, carrots and currants; saut 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 400F 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.