In a large bowl, whisk together coconut flour, sweetener, baking powder, and salt. Add eggs, butter, and vanilla and stir to combine. Add sparkling water and whisk until smooth. Let batter rest a few minutes to thicken*.
Heat a large skillet over medium high heat and brush with vegetable oil or melted butter. Scoop two or three tablespoons of batter onto skillet and spread into a 3 to 4 inch circle. Repeat until you can't fit any more pancakes into the skillet (you should be able to get 3 or 4 in).
Cook until bottom is golden brown, top is set around the edges, and a few bubbles appear in the top. Flip carefully and continue to cook until second side is golden brown. Remove from pan and keep warm on plate or baking sheet in oven, while repeating with remaining batter.
*Cook's Note: Due to variations in coconut flour, your batter may be too thin or too thick. If your batter is too thin, add an additional tablespoon of coconut flour. If too thick, add a few tablespoon of sparkling water. Your pancakes may appear flat when cooking on the first side but puff up when flipped.