Preheat oven to 350 F. Grease and flour a 6 ½ x 3-inch loaf pan.
Cream butter and sugar together until light and fluffy. Beat in egg and vanilla extract.
In a separate bowl, sift together flour, baking powder, baking soda, cinnamon and salt. Add to creamed mixture alternately with banana.
Fold in chopped white chocolate. Scrape batter into pan and spread evenly.
Bake for 30 minutes until a tester inserted in the center of the cake comes out clean.
Allow to cool 10 minutes in the pan, then turn out onto a plate.
Melt white chocolate and drizzle on to cake.