Prepare the Dough:

1. Heat the Butter and Water: In a medium saucepan, combine the water, butter, sugar, and salt. Heat over medium heat until the butter has melted and the mixture comes to a gentle boil. Remove from heat once it starts to bubble.
2. Add the Flour: Stir in the flour all at once. Use a wooden spoon or spatula to mix until the dough forms a smooth ball and pulls away from the sides of the pan. This step helps to ensure that the flour is fully incorporated and that the dough is smooth.
3. Add the Eggs: Allow the dough to cool for about 5 minutes before adding the eggs. Add the eggs one at a time, mixing well after each addition. The dough will initially seem a bit lumpy as the eggs are added, but keep stirring until it becomes smooth and elastic.
4. Add Baking Powder and Vanilla: Stir in the baking powder and vanilla extract to the dough. The baking powder will help the churros puff up as they fry.

Fry the Churros:

5. Prepare the Frying Oil: Heat about 3 inches of vegetable oil in a deep frying pan or pot over medium heat. The oil should reach 350°F (175°C) for perfect frying. Use a thermometer to monitor the temperature, or test by dropping a small piece of dough into the oil; it should sizzle and float to the top when the oil is ready.
6. Pipe the Churros: Spoon the churro dough into a piping bag fitted with a large star tip (or a resealable plastic bag with the corner cut off). Gently squeeze the dough into the hot oil, creating small 1-inch pieces of dough (poppers). Work in batches to avoid overcrowding the pan. Fry the poppers for 2-3 minutes, or until golden brown and crispy on all sides.
7. Drain the Churros: Use a slotted spoon to remove the churros from the oil and place them on a paper towel-lined plate to drain any excess oil. Let them cool slightly while you prepare the cinnamon-sugar coating.

Coat the Churros:

8. Make the Cinnamon-Sugar Coating: In a shallow bowl, combine the granulated sugar and ground cinnamon. Toss the warm churros in the cinnamon-sugar mixture until they are fully coated. This step gives the churros their signature sweet and spiced flavor.
9. Serve: Arrange the churros on a serving platter and serve immediately with your favorite dipping sauces on the side. You can serve them with chocolate sauce, caramel, whipped cream, or any other sauce of your choice for added flavor.