Preheat the oven to 325 degrees F. Lightly grease a 7 by 4 by 3-inch loaf pan with oil.
In a medium bowl, whisk together the flour, 1 cup of the evaporated cane juice, the potato starch, arrowroot, baking powder, baking soda, xanthan gum, salt, and 1 tablespoon of the cinnamon. Add the oil, applesauce, vanilla, and 1 cup of hot water to the dry ingredients. Stir until the batter is smooth. Transfer 1/4 cup of the batter to a small bowl, and add the remaining 1/4 cup of the evaporated cane juice, 1 tablespoon of cinnamon, and the remaining hot water. Stir until the mixture is creamy.
Pour contents of the medium bowl into the prepared loaf pan. Carefully drizzle the batter from the small bowl down the center of the loaf. To create the swirl, take a teaspoon and, starting from 1 end of the loaf pan, move down the length of the pan as you swirl the spoon up and down through the batter. Sprinkle the top with evaporated cane juice. Put the pan in the oven on the center rack and bake for 25 minutes. Remove from the oven and brush the top with a generous amount of oil. Return it to the oven and bake for another 15 minutes, or until a toothpick inserted in the center comes out clean and the crust is crunchy.
Let the teacake cool in the pan for 20 minutes, then gently run a knife around the edge of the cake. Cover the top of the pan with a cutting board, and invert the cake onto the board. Carefully lift the pan away and re-invert the Teacake onto another cutting board. Either cut and serve warm, or wait until it is completely cool before storing. Cover the uncut teacake with plastic wrap and store at room temperature for up to 3 days.