Cream the butter. Gradually add the granulated sugar, blending well. Add the peanut butter and egg and blend well. Combine the flour, baking soda, salt, cinnamon and nutmeg, mixing well. Add to the creamed mixture alternately with the applesauce. Pour the batter into a greased 8-inch square pan. Bake in a preheated 350 Degree F. oven for about 40 minutes or until a wooden pick inserted in the center comes out clean. Cool, in the pan, for 10 minutes and cut into squares.