Preheat the oven to 350°F. Spray a Bundt or tube pan well with nonstick spray.
In a large bowl, stir together the flours, flax seed, baking powder, cinnamon and salt. In another bowl, toss the apple chunks with lemon juice, about 1/4 cup of the sugar and a bit of cinnamon; set aside.
In a third bowl, whisk together the eggs, oil, brown sugar, sugar, tomato paste, orange juice and vanilla until smooth. Add to the dry ingredients and stir just until blended.
Pour a third of the batter into the prepared pan and smooth the top. Scatter with a third of the apples (and half the nuts, if you’re using them), then repeat with another layer of batter and apples and nuts, and a final layer of batter, then apples. (Nuts are best kept inside the cake to keep them from burning.) Pour any juices that accumulated in the bottom of the apple bowl overtop.
Bake for 1 hour and 15 minutes, until golden and springy to the touch. Cool the cake in the pan to lukewarm before inverting it onto a wire rack or plate.
Makes 1 cake; serves 24.