Bring water, butter, granulated sugar, and salt to a boil in a Dutch oven, stirring until the butter melts and the surface looks active with bubbles. Add the flour all at once and stir vigorously until the dough pulls away from the sides and forms a ball.

Cool the dough for 5 minutes, then beat in the eggs one at a time and mix in the vanilla extract until smooth and glossy. Stop when the mixture holds together and smooths out after each addition.

Fill a piping bag with the churro dough and pipe 3-inch rounds (spiraling inward like a flat disk) onto parchment. Keep the rounds even so they sandwich cleanly.

Fry the rounds in 375F vegetable oil for 2-3 minutes per side until deeply golden. Drain briefly, then immediately roll each disc in cinnamon-sugar so the coating sticks while the churros are hot.

Cool the churro discs completely before assembling so the ice cream doesn’t melt into the crust. Sandwich a scoop of vanilla ice cream between two discs and press lightly so the edges meet.

Freeze the sandwiches until firm, about 1 hour, so they slice and hold their shape. Drizzle with dulce de leche and serve immediately after freezing.