Bring water, butter, sugar, cinnamon, and salt to a rolling boil in a medium saucepan over medium-high heat. Add flour the flour all at once and stir until it comes together in a clump.
1 cup water, 1/2 cup salted butter, 1 Tablespoon granulated sugar, 1/4 teaspoon cinnamon, Pinch of salt, 1 1/4 cups all-purpose flour
Remove from heat and add the eggs, one at a time. You can do this by hand with a wooden spoon, or transfer the dough to the bowl of a stand mixer and beat them in using the paddle attachment. The dough will separate at first, but then come back together as the eggs are mixed in.
2 large eggs
Transfer the dough to a large pastry bag fitted with a rounded or closed star tip like an Ateco 849 (or try the Wilton 2D, Ateco 845, or Ateco 846). Combine sugar and cinnamon in a shallow dish and set aside.
1/2 cup granulated sugar, 1 teaspoon ground cinnamon
Heat about 2" of oil in a large pan to between 350° and 375°F. Pipe 6-inch lengths of dough into hot oil, using scissors to cut off each length of dough for a clean end. Work in batches and don't crowd the pan to prevent the oil temperature from dropping too much.
oil
Cook the churros for about 2 minutes until golden brown.
Remove the churros from the oil using tongs and drain on a wire rack or a plate lined with paper towel for 10 seconds, then roll the still-hot churros in the cinnamon-sugar mixture to coat. Serve hot with or without a dipping sauce!