In a 4-quart saucepan, combine the sugar, corn syrup, cream, milk and salt. Clip a candy thermometer to the side of the pot and cook the mixture over medium heat, stirring constantly with a heatproof rubber spatula, until the mixture reaches 236 degree F on the thermometer. Remove the pot from the heat and stir in the vanilla and root beer extracts.
Pour the mixture into a 9X13-inch baking pan (you’ll be mixing it again later). Leave the pan undisturbed to cool at room temperature for about an hour. (Do not stir during this step or the fudge can turn to sugar.)
When cool enough, pour the mixture into a large mixing bowl and mix on medium speed or by hand using a wooden spoon. If using a mixer, it will require approximately 3 minutes of mixing. Mixing by hand will take about 6 minutes. When the fudge begins to lighten in color, lose a bit of it’s shine and thicken slightly, stir in the mini marshmallows and stop mixing.
Butter a 9-inch square baking pan, pour in the mixture, and spread evenly with an offset spatula. Allow the fudge to set and crystallize for 1 hour or longer at room temperature. It will lighten in color as it cools. Cut into desired pieces and serve. The fudge should be stored tightly covered at room temperature or refrigerated tightly sealed for longer storage.