In a medium saucepan over medium-high heat, melt butter.
Stir in water, sugar, and salt. Bring to a boil.
Reduce heat and stir in flour. Continue to stir over low heat for about 1 minute.
Remove from heat and allow to cool.
Note, make sure the dough has cooled in order to prevent eggs from scrambling. Incorporate 1 egg at a time into the dough, stirring until well mixed and the dough is smooth.
Prepare a pastry bag fitted with a large star tip. Set aside.
Prepare cinnamon sugar by mixing together granulated sugar and ground cinnamon in a shallow pan.
Line baking sheets with paper towels and set aside near frying station.
Using a wok, or large saucepan, heat vegetable oil to a temperature of 350°F.
Pipe 4-inches of dough into the oil, no more than three at a time.
Fry until golden brown, using tongs to turn the churros. Note, maintaining the oil temperature at around 350°F is important. If the oil becomes too hot, the churros will brown quickly on the outside, not thoroughly cooking through.
Remove crispy churros from the oil and roll into the cinnamon sugar.
Set on prepared baking sheets to cool. Continue steps until all the dough has been fried.
Using a skewer, push through the churro from one end to the other, making sure not to push all the way through the end. This helps keep the nutella inside the churro.
In a microwave or stove top, warm nutella.
Fit a small tip to a pastry bag. Fill with nutella and pipe into each churro. Serve warm.