Preheat the oven to 325 degrees F. Lightly grease 3 (12-cup) mini-muffin pans with oil.
In a medium bowl, mix together the flour, sugar, cocoa powder, potato starch, arrowroot, baking powder, salt, baking soda, and xanthan gum. Add the applesauce, 1/2 cup oil, hot water, and vanilla to the dry ingredients and stir until the batter is smooth. Using a rubber spatula, gently fold in the chocolate chips just until they are evenly distributed throughout the batter.
Using a melon baller, scoop the batter into each prepared mini-muffin cup. Bake the brownies on the center rack for 10 minutes, rotating the tray 180 degrees after 5 minutes. Cook's Note: For a fudgier cake, bake for only 8 minutes total.
The finished brownie will have a firm edge with a soft center, and a toothpick inserted in the center will come out clean.
Let the brownies stand in the pans for 10 minutes; they are best served warm. To maintain freshness, leave the brownies in the pans until ready to serve. Cover with plastic wrap and store at room temperature for up to 3 days.