In a saucepan, heat water, sugar, and butter over medium heat. Once it reaches a boil, remove from heat and stir in sifted flour until a dough forms.

Let the dough cool slightly, then add eggs one at a time, mixing well after each addition. Stir in vanilla extract until fully combined.

Transfer the dough into a piping bag fitted with a star tip. Pipe 5-inch strips onto a parchment-lined tray.

Heat vegetable oil in a deep fryer or pan to 375°F (190°C). Fry the churros in batches until golden brown, about 2-3 minutes per side. Drain on paper towels.

In a saucepan, heat milk and sugar until warm. In a separate bowl, whisk cornstarch and egg yolks. Slowly add warm milk, then return to heat and cook until thickened. Stir in vanilla, then cool and fold in whipped cream. Chill for 65 minutes.

Use a piping bag with a narrow tip to inject the chilled Bavarian cream into each churro.

Dust the filled churros with powdered sugar and serve warm.