Preheat the oven to 350 degrees. Line three large baking sheets with parchment paper.
Toast the walnuts in a skillet on low heat for five minutes.
Sift together the flour, cinnamon, baking powder, baking soda, and salt. Set aside.
In the bowl of an electric mixer, with the paddle beater attached, cream together the butter and both sugars. Starting on low speed and then increasing to medium, beat together the butter, granulated sugar, and brown sugar. Beat until combined and lighter in color, for two to three minutes.
Add the vanilla and egg and beat until just combined. Add the sifted dry ingredients and beat in until just combined.
Stir in the apples and walnuts until just combined.
Drop one tablespoon of dough for each cookie. Space them at least two inches apart. Bake one sheet at a time for 12 minutes, or until the cookies are golden brown. Cool the cookies on a wire rack until they're completely cooled.
For the Vanilla Glaze: Mix together the sugar, vanilla, and cream. Use a piping bag or a plastic bag with the corner cut off, to apply the glaze to the cookies.