For the cinnamon sugar:
Mix the sugar and cinnamon together in a large shallow bowl.
For the churros:
In a medium saucepan, combine the sugar, butter, water, and salt over medium high heat and bring to a boil. Reduce the heat to low and stir in the flour. Stir well for 30-45 seconds over low heat, allowing the dough to dry out a little. Remove from heat. Stir eggs in one at a time, making sure to thoroughly incorporate each egg into the dough before adding the next one. Stir vigorously until dough is smooth.
Remove the dough to a pastry bag fitted with a large open star tip (I used Ateco #827). Pipe the churros out onto a parchment-linked baking sheet, piping about 4-inches long. Use scissors to cut the end for a perfect shape. Place in the fridge while you heat the oil.
Make ahead: The dough can be covered and refrigerated for up to 3 hours, or frozen for up to 1 week. Thaw for 30 minutes before frying.
In a large heavy-bottomed pot fitted with a deep-fry thermometer, heat 2-inches of vegetable oil over medium-high.
When the oil reaches 350°F, use a slotted spoon to add each piece of dough to the oil, frying only a few at a time. Fry for 5-7 minutes, or until golden brown. Test the first churro to make sure the center is cooked through and no longer doughy. Let the fried churros drain on a paper towel-linked plate before toss them in the cinnamon sugar to coat while still hot. Repeat the process with the remaining dough.
With a skewer, carve a hole through the center of each churro. Place the Nutella in a piping bag fitted with a small, narrow tip. Pipe the nutella into the churros starting from the center until it comes out the end, then flip the churro around and repeat for the other end so it is completely filled.