In a small bowl, whisk together the sugar, cinnamon and espresso powder. Set aside.
Line a baking sheet with parchment paper and dust liberally with flour. Set aside. In a heavy-bottomed saucepan, combine the water, butter, sugar, espresso powder, and salt over medium-high heat. Bring the mixture to a boil. Remove the pan from the heat and, using a wooden spoon, stir in the 1 cup of flour all at once. Return the pan to low heat and stir continuously until the mixture forms a thick dough, about 2 minutes. Transfer the dough to the bowl of a stand mixer fitted with a paddle attachment. With the machine running on medium speed, slowly add the eggs. Continue to beat until the eggs are fully incorporated and the dough is thick, about 4 minutes. Transfer the dough to a pastry bag fitted with a large star tip. Pipe the dough onto the prepared baking sheet in 4-inch long logs.
In a large heavy-bottomed saucepan, pour enough oil to fill the pan about 1/3 of the way. Heat over medium heat until a deep-frying thermometer inserted in the oil reaches 175°C. (If you dont have a thermometer a cube of bread will brown in a couple of minutes.) Using a thin metal spatula, transfer the dough, 4 pieces at a time, into the hot oil, and fry until dark-golden and crispy, about 3 minutes. Drain on paper towels and roll in the cinnamon-espresso sugar while still hot. Transfer to a serving platter and serve immediately.
Note: The churro dough can also be piped into 4-inch long pieces directly into the hot oil.