Whisk the base: In a medium bowl, whisk the yogurt, sweetener, vanilla, and salt until smooth. Taste and adjust sweetness. If the mixture is very thick, whisk in 1–2 tablespoons milk to reach a creamy, pudding-like consistency.
Optional for texture: Stir in the vodka.
You won’t taste it, but it helps prevent an icy freeze and makes scooping easier.
Chill thoroughly: Cover and refrigerate the mixture for at least 1 hour. A cold base freezes faster and forms smaller ice crystals for a creamier texture.
If using an ice cream maker: Pour the chilled base into the machine and churn according to the manufacturer’s instructions, usually 15–20 minutes, until thick and soft-serve-like.
If using a no-churn method: Spread the mixture into a shallow, freezer-safe container. Freeze for 45 minutes, then stir vigorously with a fork or whisk, scraping edges into the center.
Repeat every 30 minutes for 2–3 hours until thick and creamy.
Final freeze: Transfer to a lidded container and freeze 1–2 hours until scoopable. If it firms up too much, let it sit at room temperature for 5–10 minutes before serving.