Place water, 2 tablespoons softened butter, 2 tablespoons sugar, vanilla, and salt in a medium saucepan. Heat over medium heat until butter is melted and stir occasionally until mixture boils.
Turn off the heat and remove pan from the stove. Stir in the flour with a wooden spoon. A thick paste will form. Make sure to do this off the heat and off the stove, so that the mixture can cool as you stir it.
Transfer the dough to the bowl of a stand mixer and let sit 1 minute to cool. Attach the paddle attachment and add eggs, one at a time, mixing well after each addition (work fast to avoid cooking the eggs). You can also use a large bowl with a hand mixer but work fast.
Place the churro batter in a large pastry bag fitted with a star or 1M tip.
Heat oil to 350°F in a large pot or saucepan over medium-high heat. Use a thermometer to keep track of the temperature. Place paper towels on a cookie sheet near the stove. Stir together cinnamon and sugar for coating.
Pipe churros in desired size into the oil. Use kitchen scissors to cut the dough at the pastry tip, being careful of the hot oil. Cook 3-5 minutes, depending on size, using a slotted spoon to turn them carefully about halfway through. Make sure to monitor the temperature of the oil and adjust the stove heat throughout cooking, and do not crowd the pan. Depending on pan size you can fry 2-4 at the same time.
Remove from the oil with a slotted spoon and place on cookie sheet to drain. Cool slightly, or until you can handle them.
Toss the churros in cinnamon sugar. These are best served immediately.