In a medium saucepan, combine the milk, cream, sugar, and salt over medium heat, stirring often to dissolve the sugar.
In a small bowl, beat the egg yolks.
Once the milk mixture is steaming, but not yet at a boil, slowly pour about 1/4 cup (60 milliliters) into the eggs while constantly whisking.
Once incorporated, slowly stream in and whisk another 1/2 cup (120 milliliters).
Slowly pour the mixture back into the saucepan over medium-low heat while whisking. Cook while continuing to stir until just thickened enough to coat the back of a spoon, 170-180˚F (77˚C-82˚C). Be careful not to overcook or it will curdle.
Remove from heat and whisk in the vanilla bean paste.
Pour the mixture through a fine mesh strainer into a large bowl.
Allow to cool to room temperature.
Arrange the marshmallows in a single layer on a foil-lined baking sheet. Place under a broiler set to low and toast until golden brown. Set aside and cool to room temperature.
Once cooled, transfer the marshmallows to a large blender. If they are too sticky to remove, place the cooled baking sheet in the freezer for a few minutes.
Add the cooled custard mixture to the marshmallows in the blender and blend until completely smooth.
Transfer to a large bowl, cover, and refrigerate until chilled, 4 hours to overnight.