In a medium saucepan, add 1 cup water, ½ cup unsalted butter and ¼ teaspoon salt. Bring to a boil and stir until the butter is melted and the salt is completely dissolved.
Remove from heat and gradually add 1 ½ cups flour. Stir until flour is fully incorporated. It will start to look like custard, then doughy. Watch that it does not get too thick; it will be difficult to pipe later. Transfer into a piping bag fitted with a large star tip (warning: dough will be hot). Set aside.
Fill another saucepan with oil - at least 2 inches deep - and wait until hot enough to use for frying. If using a deep fryer, set at 320F and wait until ready. Get a baking sheet ready by placing several pieces of paper towels on it. This is where you'll place the fried churros later to drain excess oil.
When ready to fry, carefully pipe and drop 3-inch pieces of churros directly into the oil (once you've piped the length you need, drop the dough into the fryer by cutting the end of the dough from the piping tip with a pair of kitchen scissors; be careful so that hot oil does not splatter on you). Fry churros until golden brown (about 3 minutes). Remove from oil and let dry on baking sheet.
For the Coating:
While churros are drying, put ¼ cup granulated sugar and ½ teaspoon ground cinnamon in a large Ziploc bag and shake until combined. Put 2-3 pieces of churros in the bag and gently shake until evenly coated. Repeat until you've coated all churros.
For the Chocolate:
In a medium saucepan on medium heat, add ⅓ cup chocolate, ¾ cup milk and 2 tablespoons granulated sugar. Stir until chocolate is melted. Switch to low heat and bring to a simmer. Dissolve 1 ½ teaspoons cornstarch in the remaining ¼ cup milk and add to the melted chocolate. Stir until the chocolate thickens (when you lift the spoon you get a smooth drizzle of chocolate and not choppy drops).
Remove from heat, add a pinch of sea salt and give the chocolate one final stir.
Notes
When frying churros, only fry 3 churros max at a time. This will ensure each one is fried evenly.
It is best to make the chocolate dip right before eating the churros. If the chocolate cools and seizes, you can make it smooth again by microwaving it for a few seconds and giving it another stir.