Preheat oven to 375°F.
Peel the apples and core them with a melon baller, leaving the bottom intact.
In an 8x8x2-inch glass baking dish place the apples and 2 tablespoons water. Cover loosely with waxed paper and microwave on high for 3 to 5 minutes or cover loosely with foil and bake in the oven for 15 minutes. Remove and let cool. Apples should still be firm.
In a blender or a food processor fitted with a steel blade, combine the ginger snaps and pecans. Process until mixture resembles a coarse meal. Set aside.
Cut the phyllo dough sheets into a dozen 12×12-inch squares (there will be 3 squares for each apple). Cover phyllo with a damp dish towel until you are ready to use it so that it does not dry out and become brittle. Place 1 square on a flat surface and brush lightly with butter. Stack two more squares, buttering each one, and place an apple in the center. Fill the core of the apple with 1/4 of the gingersnap/pecan mixture, and sprinkle 1 teaspoon brown sugar over the top. gently lift the four corners of the phyllo squares and bring them together, dampening with water and twisting to seal. repeat with the remaining phyllo sheets and apples.
Place the apples on a lightly greased cookie sheet and bake for 45 minutes, or until golden brown. serve warm or cool.