In a medium saucepan, combine the water, butter, and vanilla extract. Heat over medium heat until the butter melts completely.
In a separate bowl, mix together the flour, sugar, baking powder, and salt. Gradually add the flour mixture to the butter mixture, stirring continuously until a dough forms and pulls away from the sides of the pan.
Remove the dough from the heat and let it cool slightly for about 5 minutes. Then, transfer it to a piping bag fitted with a star tip (or a zip-top bag with the corner snipped off).
In a large, deep skillet or pot, heat oil over medium-high heat (about 350°F / 175°C).
Carefully pipe small bite-sized pieces of dough into the hot oil, cutting them with scissors into 1-inch lengths. Fry in batches, making sure not to overcrowd the pot. Fry until golden brown and crispy, about 2-3 minutes.
Using a slotted spoon, remove the churro bites and drain on paper towels to absorb excess oil.
In a small bowl, mix together the sugar and cinnamon for the coating. While the churro bites are still warm, roll them in the cinnamon sugar mixture until fully coated.
Serve warm and enjoy your delightful bite-sized churros!