Grease and lightly flour an 8x8 inch pan. Preheat oven at 350°F (180°C).
In a medium sized bowl, combine flour, baking powder, and baking soda. Set aside.
In a large bowl cream butter and sugar until light and fluffy. Beat in egg and vanilla essence. Add flour mixture and half and half and beat on low speed until just combined. Fold in apples and dates.
Pour batter into prepared pan. Bake for one hour or until a wooden pick inserted in the center comes out clean.
Cool on wire rack for 10 minutes. Remove from pan and allow to cool completely.