Bring the oil in a deep fryer or large heavy pot to a temperature of 375 degrees F, making sure it is properly heated for frying.
Create a vegan flax egg by mixing flax seeds and water in a small bowl. Set the mixture aside for 10 minutes.
Combine flour, sugar, baking powder, and salt in a separate bowl. Whisk the ingredients together until evenly mixed.
Pour in the dairy-free milk, flax egg, and vanilla extract. Use a whisk to combine the ingredients just until they are incorporated.
Using a funnel, carefully pour the mixture into the funnel while covering the opening with your finger to prevent it from flowing out.
Carefully remove your finger from the opening of the funnel while holding it over the hot oil. Use a smooth and controlled motion to create a spiral or free-form lattice design as the mixture flows out of the funnel.
Allow the mixture to cook for approximately 1-2 minutes, or until it turns a beautiful golden color. Use a pair of tongs to carefully flip it over to the other side.
Using tongs, carefully lift the cooked mixture from the oil and transfer it to a cooling rack or a plate lined with paper towels. Let it cool for about 5 minutes before serving or further handling.
Repeat the previous steps with the remaining batter.
Once the funnel cakes have cooled for 5 minutes, sprinkle them with powdered sugar or any other desired toppings.