In a medium saucepan over medium heat combine 1 cup water, 1/4 cup whole milk, 1/8 cup (2 tbsp) unsalted butter, 1 tablespoon granulated sugar, and 1/4 teaspoon fine sea salt. Bring to a gentle simmer and stir until butter fully melts and mixture is hot but not boiling.

Remove the pan from heat and add 1 cup all-purpose flour all at once. Stir vigorously with a wooden spoon until the mixture forms a smooth ball and pulls away from the sides of the pan (about 1 minute). Return pan to low heat and cook, stirring constantly, for 30–60 seconds to dry the dough slightly.

Transfer the dough to a bowl. Let it cool 3–4 minutes so it is warm but not hot (so eggs won't scramble). Beat in 2 large eggs, one at a time, mixing thoroughly after each addition until the batter is smooth, glossy, and pipeable. The final consistency should be thick but soft enough to pipe through a large star tip.

Heat oil

In a heavy-bottomed pot or deep fryer, heat about 2 cups vegetable oil to 350°F (175°C). If you don't have a thermometer, heat until a small piece of dough sizzles and rises steadily.

Fit a piping bag with a large open star tip (about 1/2"–3/4" diameter) and fill it with the churro dough. Pipe 4–5 inch long strips onto parchment or a flat surface if you will cut them after frying; or pipe directly into the hot oil by holding the bag close to the oil and using scissors or a knife to release the dough into the oil, forming 4–5 inch strips. Fry in batches, turning occasionally, until golden brown and crisp, about 2–3 minutes per side.

Use a slotted spoon to transfer fried churros to a wire rack set over a sheet pan to drain briefly (do not stack). Reserve several whole churro strips intact for sandwich shells and break any extra pieces into crumbles for coating/texture (set aside 1/2 cup crumbles).

Cinnamon Sugar Coating

While churros are still warm (but not oily hot), combine 1/2 cup granulated sugar and 2 teaspoons ground cinnamon in a shallow bowl. Optionally brush each churro very lightly with 1 teaspoon melted salted butter to help the sugar adhere; then roll the churros in the cinnamon-sugar until evenly coated. Place coated churros back on the rack to cool until just warm. Reserve any broken pieces as churro crumbles.

Filling & Assembly

Slightly soften 2 cups of vanilla ice cream at room temperature for 5–10 minutes so it is scoopable but not melted. Gently fold 1/2 cup churro crumbles into the ice cream to distribute crunch (reserve a small handful for finishing).

Spread approximately 2 tablespoons dulce de leche on the flat inside face of each churro strip that will function as a top or bottom for the sandwich. If your churros are fully round, split gently lengthwise with a serrated knife to create flat faces, or press two matching strips together.

Place about 1/4 to 1/3 cup of the churro-crumble-studded ice cream onto one churro shell (depending on size), smoothing the top so it will meet the other shell. Top with another churro shell, pressing gently to create a sandwich. Wipe away any excess melting ice cream.

Working quickly, roll the exposed ice cream edges in remaining churro crumbles and press lightly so they stick. If desired, drizzle a little extra dulce de leche over the top of the sandwich or pipe a thin line between the shells before closing for more caramel-rich flavor.

Place assembled sandwiches on a parchment-lined tray and freeze upright or flat for at least 1 hour to firm up before serving. For best texture, serve within 24–48 hours.

To serve, remove from freezer and let stand 2–3 minutes, then enjoy. If you prefer warmer churro shells, warm the shells briefly (5–8 seconds per side in a microwave on low power or 30–45 seconds in a preheated 350°F oven), fill with very cold ice cream, and refreeze as above.