To stabilize, you use campden tablets (1 crushed tablet per gallon) and potassium sorbate (1/2 tsp per gallon of wine). I'd pull out some of the wine with a wine thief or turkey baster, and then mix up the sorbate and campden in that. Stir until dissolved. Then put that in the receiving carboy and rack your wine into it. Wait about 10 days and then rack if necessary. Sometimes, there will be dusting of sediment after you stabilize. Then, it's easy to sweeten it to taste. I like to pull out a sample, and add a simple sugar syrup until I like the taste. You could use honey, if you'd rather, or a combination. Then take the sg of your sample and sweeten the whole batch to that sg. A word of caution, here, though- make it just a little less sweet than you actually like it. It seems to get sweeter and sweeter after a while. So, if you really like it at 1.010, I'd recommend sweetening to 1.008 or so.
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