Thread 24 marshmallows onto skewers and toast over an open flame until golden and charred in spots. (Alternatively, place the marshmallows on a baking sheet and broil, turning with a spoon, until toasted all over.)
Put the toasted marshmallows, cream, milk, vanilla and salt in a saucepan and cook, stirring constantly, over medium heat until the marshmallows melt. (Some charred bits may remain.) Let cool 20 minutes.
Preheat the oven to 325 degrees F. Whisk the eggs and egg yolks in a bowl. Slowly whisk in 1 cup of the cooled marshmallow mixture, then whisk in the remaining mixture, being careful to not beat in too much air. Pour through a fine-mesh sieve into a large liquid measuring cup.
Arrange six 4-ounce ramekins in a roasting pan. Divide the custard among the ramekins. Transfer the roasting pan to the oven and add enough hot water to reach halfway up the sides of the ramekins. Bake until the custards are set but wobbly in the center, 30 to 35 minutes. Remove from the oven and let sit in the water bath until cool enough to handle. Remove the custards from the water bath and let cool to room temperature, then cover with plastic wrap and refrigerate until firm, at least 2 hours or overnight.
Preheat the broiler. Transfer the custards to the freezer to chill, 15 to 30 minutes. Meanwhile, pulse the remaining marshmallows and 3 tablespoons hot water in a food processor until creamy, about 1 minute. Top each custard with 1 to 2 tablespoons of the marshmallow topping and gently spread to the edges with damp fingertips. Broil until the tops are bubbly and dark brown. Transfer the creme brulees to the refrigerator to chill, about 1 hour. Serve cold.