Pour Dr. Pepper into a saucepan and bring to a gentle simmer over medium heat.

Cook uncovered until reduced to about 1/2 cup, about 20–25 minutes.

Remove from heat and cool completely.

In a large bowl, whisk heavy cream, milk, sugar, vanilla extract, and salt until sugar dissolves.

Whisk in the cooled Dr. Pepper reduction until fully combined.

Cover and refrigerate the mixture for at least 2 hours.

Churn in an ice cream maker according to manufacturer’s instructions until soft-serve consistency.

Transfer to a freezer-safe container and freeze 2–3 hours to firm up.

If not using an ice cream maker, freeze in a shallow container and stir every 30–45 minutes until smooth and scoopable.