Prepare the cinnamon sugar.
In a shallow bowl, combine the sugar and cinnamon. Set aside.
Make the dough.
In a saucepan over medium heat, combine the water, 2 tablespoons vegetable oil, sugar, and salt. Bring to a boil.
Reduce the heat to medium-low and add the flour all at once. Stir firmly until the mixture forms a dough ball and no dry pockets of flour remain.
Cover for about 1 minute, then remove from the heat.
Rest the dough.
Add the remaining tablespoon of vegetable oil and work it into the dough with a sturdy spoon.
Transfer the dough to parchment paper. Let it cool enough to handle, then gently fold it until smooth. Cover and rest for 10 minutes. The dough should still be warm enough to pipe easily.
Pipe the hearts.
Cut parchment paper into individual squares large enough to hold each heart.
Transfer the dough to a sturdy piping bag fitted with a large open star tip. Pipe hearts onto the parchment, joining the ends and gently pressing them together so they stay connected. Use clean kitchen scissors to trim the dough as needed.
Let the shaped churros rest for 30 minutes, loosely covered to prevent drying.
Heat the oil.
Heat about 2 inches of vegetable oil in a deep, heavy pan to 350°F (175°C), leaving plenty of space above the oil.
Fry the churros.
Working in small batches, carefully lower a churro into the oil with its parchment square, keeping your fingers away from the oil. Once the paper releases, remove it with metal tongs.
Fry for about 4–5 minutes, turning occasionally, until golden brown and cooked through. Cooking time will vary with the thickness of the hearts.
Coat and serve.
Remove the churros with a slotted spoon and briefly drain on paper towels.
While still warm, gently roll in the cinnamon sugar. Serve immediately.