Preheat the oven to 350F. Line the bottom of a 9-inch springform pan with parchment paper and lightly grease the sides. Alternatively, line a regular 9-inch round cake pan with parchment paper. If you're using a springform pan, place it on top of a baking tray (this will catch any drippings in the event that the pan leaks).
In a small mixing bowl, whisk together the flaxseed meal and the filtered water. Let stand for 5 minutes, or until thickened.
In a large mixing bowl, use a stand mixer or hand mixer to beat together the vegan butter and brown sugar on high for 2 minutes (set a timer). Add the thickened flaxseed mixture, vinegar, and vanilla, and beat again for 30 seconds, or until thoroughly incorporated.
In a medium mixing bowl, whisk together the flour, baking powder, and sea salt. With the mixer off, add the dry ingredients to the butter mixture. Slowly turn the mixer on low, increasing to medium, and beat for 30 seconds, or until thoroughly combined. The batter should be very thick and fluffy.
Fold the chopped RaveⓇ apples into the batter.
Evenly spoon the batter into the prepared pan, using a spatula to smooth. Sprinkle the top with a thin layer of cane sugar.
Bake for 40 to 50 minutes, or until a toothpick inserted into the center of the cake comes out clean.
Transfer the cake pan to a heat-safe cooling rack. If you used a springform pan, release the wall of the pan and remove (this allows the cake to vent steam and expedites the cooling process). Cool completely.
If you'd like to ice the cake, vigorously whisk together about two cups powdered sugar with a few tablespoons filtered water, adding more powdered sugar as needed to thicken or more water as needed to thin. Drizzle over the cooled cake.
Slice and serve.
Leftovers will keep for up to three days in the refrigerator.