Combine the almond flour, tapioca starch, and salt in a small mixing bowl. Add the whisked egg and water to the flour mixture and stir to combine. Add the melted coconut oil and knead the oil into the dough to combine.
Dust a sheet of parchment paper lightly with arrowroot flour. Place the ball of dough on the parchment, and lightly press the dough down with your hands to flatten.
Dust a rolling pin with tapioca starch, and roll the dough into a very thin sheet, about ¼- to ⅛-inch thick. You want the dough to be as thin as possible, while still being able to work with it. Using a chef knife or pizza cutter, slice the dough into 1x2-inch pieces.
In a heavy, high-walled saucepan, heat the frying fat to 350°F. (We highly recommend monitoring the temperature using a candy thermometer. If you don’t have a candy thermometer, you can test the heat using a small piece of dough.)
Carefully drop the strips of dough, one at a time, into the hot oil, and fry the dough for 2-3 minutes per side, or until golden brown. Remove the fried wontons from the oil, sprinkle with salt to taste, and allow to cool on a wire rack.