Prepare egg alternative for two eggs by combining arrowroot, vegetable oil, and water in a small bowl
In a medium bowl begin to cream the egg and sugar, once mixed slowly add in milk and vanilla
Once wet ingredients are mixed, whisk in baking powder and flour until a thin pancake-like consistency
Transfer batter into a squeeze bottle and begin to heat up cooking oil on medium heat over the stove
Once cooking oil reaches 365°, begin to dispense batter by drizzling into the oil to form a funnel cake shape (about 9" in diameter)
Fry cake for 2-3 mins or until light golden brown and flip cake to fry for 2-3 more mins
Once light golden brown on both sides remove the cake from oil and let rest on paper towels or baking rack
For serving, transfer funnel cake to plate and sift confectioners sugar and add any favorite toppings on funnel cake and enjoy