Preheat the oven to 350 degrees F. Grease a 10- or 12-inch cast-iron skillet with oil and set aside.
Combine the flours, baking powder, flax meal, cinnamon, baking soda and salt in a mixing bowl, and stir with a fork or whisk until well combined. Add the maple syrup, sparkling water, vanilla and oil and stir well with a fork to combine.
Grate the apples with a box grater or a food processor with a grater attachment blade. Add the apples and walnuts to the batter and stir to combine.
Spoon the batter into the prepared skillet and spread evenly. Bake until the top is lightly browned, 20 to 30 minutes. Let cool 5 minutes, then slice into 8 wedges and serve.