Preheat the oven to 350˚F and line an 8 x 8-inch baking pan with parchment paper.
In a large bowl, mix together the apples, pears, flax meal, water, sugars, oil, yogurt and vanilla extract.
In a medium size bowl whisk together the flours, baking soda, baking powder, cinnamon, nutmeg and salt.
Add the dry flour mixture to the wet apple mixture and stir until just combined. Add in the chopped nuts and cranberries and fold them into the mixture.
Scrape the batter into the prepared baking pan and bake the cake in the center of the oven for 35 to 40 minutes. Insert a wooden skewer or toothpick into the center of the cake to make sure it is fully cooked. If the stick comes out clean the cake is ready.
Allow to cool in the pan for about 30 minutes then carefully remove the cake from the pan and transfer to a wire rack to cool fully.
While the cake is cooling make the frosting. Place all the frosting ingredients into mixer and whisk until smooth, soft and fluffy. Keep refrigerated until required. Once the cake has cooled spread the frosting over the top.