To make the custard base, combine the whole milk and sugar in a saucepan over medium high heat. Heat the mixture until steaming and bubbles appear at the edges, do not boil. Meanwhile, whisk together the egg yolks in a large bowl. Slowly add the heated milk mixture to the egg yolks while whisking constantly. Pour the mixture back into the saucepan and cook over medium heat until thickened and coats the back of a spoon, stirring frequently. Pour mixture through a mesh strainer into a large bowl. Add the heavy cream, vanilla extract, and salt. Set aside.

Spread the marshmallows out on a sheet pan lined with parchment paper or a silpat. Toast the marshmallows with a kitchen torch or an oven broiler. If you use a broiler, place the oven rack as high as possible and watch the marshmallows very closely to ensure they don't burn. Rotate the marshmallows so that they are evenly toasted on each side.

In a blender, add the custard mixture and the toasted marshmallows and puree until smooth. Chill completely in the fridge. Freeze in an ice cream machine according to the manufacturer's instructions. Let harden in the freezer for an addition few hours before serving.