Stir together the sugar, corn syrup, water, and salt in a small saucepan over high heat. Bring the mixture to a boil, stirring often, until the it reaches 240° F on a candy thermometer. Be careful not to let the mixture bubble over: Turn the heat down if you need, and keep a watchful eye over it. This might take a little longer than you think, but just keep at it. Mine took about 10 minutes, but when you're standing there watching it, it feels like an eternity. It got stuck at around 220 for what seemed like forever, but then it eventually got up to 240.
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. You want to have the egg whites whipped and ready to go, 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, which is what I did.
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, a bit at a time -- seriously, do not do more than 2 tablespoons at a time.
Increase the speed to medium-high and whip until the marshmallow fluff is stiff and glossy, about 7 solid minutes. Don't try to speed this process up! Add in the vanilla and whip 2 minutes more. Use the fluff immediately, or store it in an airtight container and refrigerate for up to 2 weeks. I made my fluff about 4 hours ahead of time, stored it in an airtight container, and served it on its own with graham crackers and chocolate later in the day at a barbecue.