In a large bowl, whisk together the gluten-free flour, baking powder, salt, and sugar.
In a separate bowl, beat the eggs, milk, and vanilla extract until smooth.
Gradually combine the wet ingredients with the dry ingredients, whisking until a smooth batter forms. The consistency should be pourable but slightly thick.
Heat the oil in a deep skillet over medium heat until it reaches 350°F (175°C).
Using a ladle or squeeze bottle, drizzle the batter into the hot oil in a circular, swirling motion to form a funnel cake shape.
Fry for 2–3 minutes per side, until golden brown and crisp.
Remove with a slotted spoon and place on paper towels to drain excess oil.
Repeat with remaining batter.
Dust with powdered sugar or add your favorite toppings before serving.