In a large mixing bowl, combine the flour, sugar, baking powder, and salt.
Mix the Wet Ingredients:

In a separate bowl, whisk together the eggs, milk, and vanilla extract.
Combine Mixtures:

Gradually add the wet ingredients to the dry ingredients, stirring until the batter is smooth and free of lumps.
Heat the Oil:

Heat about 2 inches of vegetable oil in a deep skillet or fryer to 375°F (190°C).
Prepare for Frying:

Pour the batter into a squeeze bottle with a wide opening or a piping bag fitted with a large round tip.
Fry the Funnel Cake Sticks:

Carefully squeeze the batter into the hot oil in long, thin strips, cooking a few at a time to avoid overcrowding.
Fry each strip for 2-3 minutes on each side or until golden brown and crispy.
Drain and Dust:

Remove the funnel cake sticks with a slotted spoon and place them on paper towels to drain.
Dust the hot sticks generously with powdered sugar before serving.