Preheat oven to 350F. In a medium bowl, mix together the butter and 1/3 cup of sugar. Add in the 1 cup flour and mix with a fork until crumbly. Place the mixture in the bottom of a 9x13" pan and pat out evenly. For thicker bars you can use a 9x9" pan. Bake in the oven for 15 min. or until golden. Remove to cool slightly.

Meanwhile, add the eggs to a large bowl and beat well; add in the 2/3 cup sugar and the vanilla and mix well. In a small bowl, whisk together the dry ingredients, baking powder, remaining 1/3 cup flour, and salt. Add this to the egg mixture. Carefully fold in the pineapple, coconut, nuts and cherries. Spread over the baked and slightly cooled crust. Bake for 30 min. Cool completely on a rack and then cut into squares.