Preheat the oven to 350°.
In a medium bowl, sift together the flour, baking powder, baking soda, salt, cinnamon and pumpkin pie spice. Set aside.
In a mixing bowl, cream the butter and sugars together, and add the vanilla. Beat in the egg. Add the flour mixture to the butter mixture and mix just until it begins to come together. Add the ginger, oats and carrots and mix until well combined.
Scoop even spoonfuls onto a greased pan and bake for 12 to 15 minutes, just until the edges begin to brown. Don’t overbake; the cookies should be soft.
Cream Cheese Filling: Beat together 4 ounces cream cheese; 2 tablespoons unsalted butter, softened; ½ cup powdered sugar and a pinch of salt until smooth. Fill the cookies, sandwich style.