Grease a shallow 9" square baking pan. To make the topping, place the sugar and butter in a small saucepan and heat gently, stirring, until melted. Pour into the pan and arrange the apple slices over the mixture.
2To make the brownies, place the butter and sugar in a large bowl and beat together until light and fluffy. Gradually beat in the eggs. Sift together the flour, baking powder, baking soda, and apple pie spice, and fold into the mixture. Stir in the apples and nuts, then pour into the pan.
3Bake in the preheated oven for 35 to 40 minutes, or until firm and golden. Let cool in the pan for 10 minutes. Cut into squares.