Grease a tube pan lightly with coconut oil.
In a large bowl, whisk together the flours, sugar, baking powder, and salt.
Whisk in the eggs, oil, apple juice, and vanilla extract, then use a spoon to make sure the batter is smooth and the dry ingredients are well incorporated. Let batter rest while you prepare the pears.
Peel and core the pears, then cut the pieces into ¼-inch chunks. Mix the pears with the cinnamon and brown sugar.
Then, spread half of the batter in the tube pan and sprinkle half of the pear mixture evenly across it. Add the rest of the batter and top with the remaining pears. Heat oven to 350℉ and let batter rest while the oven heats.
Place pan in the oven and bake for 1 hour 15 minutes-1 hour 30 minutes, checking frequently, until a tester inserted comes out clean, the top is slightly firm when gently pressed, and the edges are starting to come away from the pan.
Remove from oven and cool in pan for 15 minutes on a wire rack, then turn out onto a rack to cool completely. Cake will keep, well wrapped in the fridge, for up to five days.