Preheat the oven to 350°F (180°C, or gas mark 4). Line a rimmed baking sheet with parchment paper, allowing the parchment to hang over the edges of the pan. Spread the mini marshmallows evenly on the baking sheet. Bake until they are dark brown in color, with some marshmallows beginning to burn, about 12 to 14 minutes. Remove from the oven and set aside.
Fill a large bowl with ice water and set it aside. In a medium saucepan, combine the milk, heavy cream, and sugar, then place it over medium heat. Bring the mixture to a low boil, cooking until the sugar dissolves, about 3 minutes.
Reduce the heat to low and add the toasted marshmallows, whisking until they melt, about 5 minutes. Pour the mixture into a medium bowl and whisk in the salt. Set the bowl in the ice water bath to cool for about 20 minutes, whisking occasionally. Once cooled, add the vanilla. Cover and chill in the refrigerator overnight.
Once chilled, pour the ice cream base into an ice cream maker and churn according to the manufacturer’s instructions. Pack the churned ice cream into a freezer-safe container and freeze until firm, at least 4 hours.
Serving Suggestion: Top with a scoop of Cow Patty Ice Cream (page 84) or any chocolate ice cream. Sprinkle with graham cracker crumbs for a delightful s’more experience in a bowl.