1) Peel the mangoes, discard the pits, and process in a food processor or blender until nearly smooth; a few small lumps can remain. Measure to make sure you have 3 to 3 1/2 cups purée.
2) Add the water, syrup or honey, lemon or lime juice, and salt, stirring to combine.
3) Place the mixture in the refrigerator, and chill thoroughly; overnight is best. If you're going to use an ice cream maker, make sure the freezer bowl is in the freezer. Again, overnight is best.
4) Next day, pour the mango mixture into the bowl of the ice cream maker. Flip the switch, and let the sorbet freeze for 20 to 25 minutes, until thickened to the consistency of soft-serve ice cream.
5) If you're using the vodka or liqueur, add it at the end.
6) Transfer the sorbet to a freezer container, cover it, and place in the freezer compartment of your refrigerator until it's as hard as you like; this will probably take a minimum of several hours.
7) To make the sorbet without an ice cream maker: Place the mango mixture in a shallow pan; an 8" x 8" or 9" round cake pan are both good choices. Place the pan in the freezer. There's no need to cover it.
8) After 2 hours, use a fork or spoon to stir it around, bringing the frozen edges into the center. Return to the freezer.
9) Continue to stir every hour or so, until the sorbet is nearly as firm as you like. This may be as little as 4 hours total, start to finish; or it may take longer, depending on the temperature of your freezer.
10) Once the sorbet is entirely icy (like a slush drink), add the alcohol, if you're using it. Rather than add the alcohol while the sorbet is still in its shallow pan, transfer the sorbet to a lidded storage bowl. Stir in the alcohol, then cover the bowl and place it in the freezer. Let the sorbet "ripen" (freeze), undisturbed, for several more hours, until it's as hard as you like.
Yield: about 3 1/2 cups sorbet.