Make the Vanilla Cream Filling:
In a medium saucepan, whisk together the heavy cream, milk, sugar, and cornstarch. Cook over medium heat, whisking constantly, until the mixture thickens to a pudding-like consistency (about 5–7 minutes). Remove from heat, stir in the vanilla extract, and transfer to a bowl. Cover with plastic wrap (touching the surface to prevent a skin from forming) and chill until ready to use.
Prepare the Churro Dough:
In a medium saucepan, combine water, sugar, butter, and salt. Bring to a boil, then remove from heat. Add the flour all at once and stir vigorously until the dough forms a ball. Let cool for 5 minutes, then add the egg and vanilla extract. Mix until smooth.
Heat the Oil:
Heat vegetable oil in a deep frying pan or pot to 375°F (190°C).
Pipe and Fry the Churros:
Transfer the dough to a piping bag fitted with a large star tip. Pipe 4–5-inch strips of dough directly into the hot oil, cutting with scissors. Fry 3–4 churros at a time for about 2–3 minutes per side, or until golden brown. Remove and drain on paper towels.
Coat the Churros:
In a small bowl, mix the granulated sugar and cinnamon. Roll the warm churros in the mixture until fully coated.
Fill the Churros:
Use a skewer or chopstick to create a hole in the center of each churro. Transfer the chilled vanilla cream to a piping bag fitted with a small round tip and pipe the filling into each churro.
Serve and Enjoy:
Your Vanilla Cream Filled Churros are ready to enjoy! Serve warm for the best texture and flavor.