Create the base mixture: In a medium saucepan, combine water, butter, and 2 tablespoons of erythritol. Place over medium heat and bring to a gentle simmer, stirring occasionally until butter melts completely and erythritol dissolves fully.

Form the churro dough: Remove saucepan from heat immediately. Add almond flour, coconut flour, baking powder, and xanthan gum all at once. Stir vigorously with a wooden spoon until a cohesive dough forms into a smooth ball.

Cool and incorporate wet ingredients: Let dough cool for 2-3 minutes. Add vanilla extract and crack in the egg. Mix thoroughly until egg is fully incorporated and dough becomes smooth and pipeable.

Prepare for frying: Transfer churro dough into a piping bag fitted with a large star tip. Pour coconut oil into a deep pot or heavy-bottomed skillet (about 2-3 inches deep). Heat oil over medium-high heat until it reaches 350°F.

Pipe and fry the churros: Carefully pipe 4-5 inch strips directly into hot oil, using kitchen scissors to cut dough from piping bag. Fry 3-4 churros at a time for 2-3 minutes per side until golden brown. Use a slotted spoon to flip halfway through. Transfer to paper towel-lined plate to drain.

Apply the cinnamon sugar coating: Mix remaining 2 tablespoons erythritol with cinnamon in a shallow bowl. While churros are still warm, roll each one generously in the mixture, coating all sides evenly. Serve immediately.