Stir together the sugar, corn syrup, water, and salt in a small saucepan over high heat. Bring to a boil, stirring occasionally, until the mixture reaches 240°F on a candy/fat thermometer.
Place the egg whites and cream of tartar in the bowl of a stand mixer fitted with a whisk attachment. Start whipping the egg whites to soft peaks on medium speed. (The goal is to have the egg whites whipped and ready, waiting for your syrup to be drizzled in. If they’re whipping faster than your syrup is coming to temperature, just stop the mixer until the syrup is ready.)
When the syrup reaches 240°F, reduce the mixer speed to low and slowly drizzle about 2 tablespoons of syrup into the egg whites to warm them. (If you add too much syrup at once, the whites will scramble.) Slowly drizzle in the rest of the syrup. Increase the speed to medium high and whip until the marshmallow crème is stiff and glossy, about 7 minutes. Add in the vanilla and whip 2 minutes more. Use immediately or refrigerate stored in an airtight container for up to 2 weeks.