Preheat the oven to 350 degrees F. Grease a 9-by-11-inch baking dish and set aside.
Place the carrots and yams in a food processor and process on high until finely chopped. Add the cream, turbinado sugar, cinnamon, nutmeg, salt and eggs to the basin and pulse until well blended.
Pour the mixture into the greased baking dish and spread evenly with a rubber spatula. Top with the miniature marshmallows and bake until the marshmallows become puffed and golden brown, 25 to 30 minutes.