Toast the marshmallows over the flame of a gas stove or broil them in the oven until they are light brown and puffed up. Do not let the marshmallows burn. Set them aside.

Combine the cream, milk, sugar and corn syrup in a saucepan and bring to a boil.

Remove from the heat and add the toasted marshmallows, stir until melted.

Transfer the mixture to a metal bowl and refrigerate until completely cooled, at least 1 hour and up to overnight.

Freeze the mixture in an ice cream maker according to the manufacturer's instructions.