Preheat oven to 400 degrees. Grease (1) 8-inch cake or pie pan. Set aside.
Sift together the flour, baking powder, salt and sugar. Add the beaten egg and stir until mostly combined. Add the apple and the chopped pecans and stir until a thick batter forms.
Press batter into the prepared pan. Bake for 25-30 minutes, or until golden brown and the edges of the cake slightly pull away from the edges of the pan.
Once cooled, store covered for up to 3 days. Cake will become more moist as it sits.
Notes
I recommend using a good baking apple for this recipe. Golden delicious, jonathan, braeburn, mcintosh, and jonagolds are all great options.