Add the butter to a small saucepan along with 1 cup of water. Set over a medium heat and stir with a wooden spoon until the butter has dissolved and the mixture is bubbling slightly.
Add the flour and beat into a smooth ball without any lumps. Remove from the heat. Set aside to cool for 10 minutes.
Transfer the dough to a medium bowl and beat in the eggs, one by one. At first it will feel like the mixture won’t come together, but stick at it and it will come good.
Heat enough oil to cover 1 1/2 inches at the bottom of a large, heavy bottomed casserole or skillet over a medium high heat to 375F. Meanwhile transfer the dough to a disposable piping bag fitted with a large star tip, or with a 3/4 inch hole cut in the end.
Combine the cinnamon sugar ingredients in a shallow dish and set aside.
Working a few at a time, squeeze 4-5 inch strips into the hot oil, cutting them with a pair of scissors. Fry for 8 minutes until golden, turning halfway so they cook evenly. Keep an eye on the temperature to make sure the oil does not drop below 350F. By adding the batter to the oil at the hotter temperature you’re making sure it does not cool down too much when the churros are added.
Remove the churros from the oil with a slotted spoon first onto a kitchen paper-lined plate, and then roll them in the cinnamon sugar.
Once you’ve made the first batch, allow them to cool for a minute or two before biting into them. If the outside is too hard or the middle is not cooked through, lower the temperature of the oil a little: all star tips are different and will change the surface area of the churros, making some cook faster than others. If the outside is fine but the middle is still undercooked, cook them for a minute or two longer.
Keep the churros warm while you batch cook the rest. Serve either as is, or with a chocolate dipping sauce.