Preheat oven to 350 degrees. Grease a 9-inch cake pan and line the bottom with parchment paper.
In a large mixing bowl, combine the almond flour with the arrowroot flour or tapioca starch, baking powder, and salt.
In another bowl, combine the oil, honey, vanilla, egg, and lemon zest. Add the wet ingredients to the dry and stir to combine. Gently stir in the berries. Pour the batter into the prepared pan and bake for 30 minutes.
Let cool in the pan for 10 minutes, then remove. Serve warm or at room temperature.