Preheat oven to 350 degrees. Spray a 9 x 9 baking pan with baking spray or grease with butter and lightly flour the pan.
Mix together sugar, oil and eggs in a large bowl. Whisk until smooth.
Add the flour, baking powder, nutmeg, and cinnamon. Stir in the apples and nuts. Mix until combined. The batter will be thick.
Spread evenly in 9 x 9 inch pan. Bake at 350°F for 1 hour or until a wooden skewer comes out clean.
Cool the cake at room temperature.
For the glaze:
While the cake is baking, stir all the ingredients for the glaze in a small bowl until smooth. Set aside. When the cake has completely cooled, pour the glaze over the top.