Place the butter, salt and 1 ¾ cups of water in a large saucepan. Bring to a boil, stirring occasionally. Remove saucepan from the heat.
Stirring quickly, slowly add the flour. Continue stirring until fully combined.
Return to stovetop, and cook over medium-high heat. Stirring continuously, until dough comes away from the sides of the pan. About 2-3 minutes.
Transfer dough to a medium bowl (I used my KitchenAid mixer here.) To cool mixture slightly, beat the dough at lowest setting for about minute.
Increase speed and beat in the eggs, one at a time.
Lastly add the egg white. Place a piece of plastic wrap over the top of the dough. Press the plastic so it is touching the dough’s surface.
Refrigerate until cooled to room temperature, about 10+ minutes.
While the dough is cooling, (I used my candy thermometer) heat oil to 375°, in a medium saucepan. You could use a large saucepan, but since I knew I’d be making thinner curly churros, (not long and narrow) I didn’t need a pan with a large diameter.
Cover a cookie cooling rack with paper towels. Place on top of a large cookie sheet.
With a whisk, mix together the sugar and cinnamon.
Keeping an eye on the oil temperature, spoon dough into a large pastry bag or zip closure plastic bag, using a large star tip.
Choosing your shapes willy nilly, or the traditional long narrow shape, squeeze (or squirt!) the dough into the hot oil. If necessary, cut the end of dough with a butter knife, careful not to snip the bag! Fry a few at a time; they puff up a bit as they cook. Fry over moderate/high heat, turning until evenly browned, about 4-6 minutes, depending on the thickness of your churros. Drain on the paper-lined rack for 3 minutes.
Dredge each churro in the cinnamon sugar.
Serve individually alongside hot chocolate. (Optional)