In a medium saucepan over medium heat, combine the water, 2 1/2 tablespoons of sugar, salt, and 2 tablespoons of vegetable oil. Bring the mixture to a rolling boil, ensuring the sugar is completely dissolved, then remove the pan from the heat.

Immediately pour the flour into the hot liquid all at once. Using a sturdy wooden spoon, stir vigorously until the mixture forms a smooth ball of dough and cleanly pulls away from the sides of the pan.

Transfer the dough to a plate to cool for about 5 minutes so it is safe to handle. Meanwhile, heat 4 cups of vegetable oil in a heavy-bottomed pot or Dutch oven until it reaches 375°F (190°C).

In a shallow dish, whisk together the 1/2 cup of sugar and ground cinnamon to create the sweet coating. Set this aside for later.

Place the slightly cooled dough into a strong piping bag fitted with a large star tip. Carefully pipe 4 to 5-inch strips of dough directly into the hot oil, using a pair of clean kitchen scissors to snip the dough off at the tip.

Fry the churros in small batches of 3 or 4 to avoid overcrowding the pot. Cook for about 2 to 3 minutes per side until deeply golden brown and crispy all over.

Use a slotted spoon or tongs to remove the fried churros, letting excess oil drip off, and transfer them briefly to a paper towel-lined plate. While they are still warm, roll them in the cinnamon-sugar mixture until perfectly coated, and serve immediately with warm melted chocolate.