Make the cocoa-sugar coating: In a shallow bowl, mix 1/2 cup granulated sugar with 2 tablespoons unsweetened cocoa powder and a small pinch of salt.
Add 1/2 teaspoon cinnamon if you like. Set aside.
Start the dough: In a medium saucepan, combine 1 cup water, 6 tablespoons unsalted butter, 1 tablespoon granulated sugar, and 1/4 teaspoon salt. Bring to a gentle boil over medium heat, stirring to melt the butter.
Add the flour: Remove from heat, add 1 cup all-purpose flour all at once, and stir with a wooden spoon until a thick dough forms and pulls away from the pan walls.
Dry the dough: Return the pan to low heat and cook, stirring constantly, for 1–2 minutes to evaporate excess moisture.
You’ll see a thin film on the pan bottom—that’s perfect.
Beat in the eggs: Transfer dough to a bowl. Let it cool 3–4 minutes, then beat in 2 large eggs, one at a time, plus 1 teaspoon vanilla. The dough should be glossy and pipeable but not runny.
If it’s too stiff, add 1 extra egg white or 1 tablespoon milk.
Heat the oil: Pour 2 inches of oil into a heavy pot. Heat to 350–360°F (177–182°C). Keep a thermometer handy; temperature control is key for crisp bites.
Pipe the bites: Scrape dough into a piping bag fitted with a large open star tip.
Pipe 1-inch lengths over the oil and cut with scissors, dropping each piece carefully into the pot. Work in small batches to avoid overcrowding.
Fry to golden: Cook 2–4 minutes, turning as needed, until deep golden brown and puffed. Aim for crisp but not dark.
Transfer to a paper towel–lined sheet to drain for 20–30 seconds.
Coat while warm: Roll warm bites in the cocoa-sugar mixture until fully covered. The coating sticks best while they’re still hot.
Make the Nutella dip: In a small saucepan, warm 3/4 cup Nutella with 1/4 cup heavy cream (or milk) over low heat, stirring until smooth and glossy. Add a pinch of sea salt if desired.
Keep warm on the lowest heat or in a warm bowl.
Serve: Pile churro bites on a platter, dust with a little extra cocoa-sugar, and serve with the warm Nutella dip.