In a medium saucepan, combine water, 2 1/2 tablespoons sugar, salt, and butter. Bring to a boil over medium-high heat.
Remove from heat and immediately stir in the flour until mixture forms a ball.
Let the mixture cool for 5-7 minutes, then beat in the eggs one at a time, mixing well after each addition. Add in the vanilla extract.
Transfer dough to a piping bag fitted with a large star tip.
Heat oil in a large pot or deep skillet to 375°F (190°C). Pipe dough into hot oil, forming long churros, and fry until golden and cooked through, approximately 2-3 minutes per side.
Transfer fried churros to a paper towel-lined plate to drain excess oil.
Combine 1 cup granulated sugar and cinnamon in a shallow dish. Roll churros in sugar mixture while still warm.
Serve warm with chocolate sauce, sugar, or caramel if desired.