In a medium saucepan over medium heat, combine water, butter, brown sugar, and salt. Stir until simmering and butter is melted, about 5 minutes.

Add flour to the mixture all at once and stir vigorously until a sticky dough forms, about 5 minutes.

Transfer the dough to a large bowl and let it cool for about 10 minutes. Mix in vanilla extract after cooling.

Incorporate eggs one at a time, stirring well after each addition until the dough is smooth and elastic.

Preheat the oven to 425°F (220°C) and line baking sheets with parchment paper.

Pour the dough into a pastry bag and pipe 3 to 4-inch lengths onto the prepared sheets, spacing them 2 inches apart.

Lightly spray tops with vegetable oil and sprinkle with a mist of water for steam.

Bake for 20 to 25 minutes until golden brown. Watch carefully as they puff.

Turn off oven and let churro bites cool inside with the door slightly ajar for 10 minutes.

Melt butter and brush it on churro bites, then toss in cinnamon sugar until coated. Serve warm.