Combine the lupin flour, almond flour, erythritol, baking powder, and xanthan gum in a small bowl. Whisk until the dry mixture looks even, with no visible pockets of xanthan gum or leavening.

Whisk the eggs and vanilla in a medium bowl, then blend in the dry mixture, heavy whipping cream, and water one tablespoon at a time before stirring in the mozzarella. Use 6 tablespoons of water for a thicker batter that puffs nicely in the oil, adding more only within the listed range if it will not pipe smoothly.

Pour avocado oil, coconut oil, or lard into a frying vessel to a depth of roughly 1 inch and heat it to 350°F/180°C while the batter rests. Transfer the batter to a piping bag or zip-top bag and cut a 1 cm or 1/3-inch opening for defined strands.

Pipe the batter into the hot oil in connected circles, fry until deeply golden, and gently flip to brown the second side. Move the cake to a wire rack when the bubbling is active but controlled and the swirls feel rigid to the tongs, then dust with powdered erythritol and serve right away.