Place the warm water, Swerve sweetener and cream of tartar into a saucepan over medium heat on the stove. Whisk until the ingredients are combined and dissolved.
Continue to cook the sweetened mixture until it comes to a boil.
While the sweetened mixture is cooking, add the cold water to a mixing bowl, and sprinkle the unflavored gelatin on top. Do not mix it at this point, just let it sit for 10 minutes.
When the mixture on the stove comes to a boil, continue to boil it for 2-3 minutes, but no less than 2, whisking often.
Remove the mixture from the heat once it has boiled, and whisk in the vanilla extract.
Start blending the gelatin mixture on high, and immediately pour the heated mixture into the mixing bowl with it.
Continue to beat the mixture on high for roughly 12-15 minutes, or until it has become fluffy and has peaks that hold their shape well on their own.
Immediately transfer the mixture into a parchment lined 9x9 baking dish, and smooth it into an even layer.
Allow the mixture to sit untouched on the counter at room temperature overnight. Do not disturb it, and do not refrigerate it.
Cut the finished marshmallows into pieces, and serve any way that you would like.