Cut the avocados in half, running your knife around the pit from stem to blossom end and back up again. Twist the halves in opposite directions to free the pit, and pull the halves apart. Dislodge the pit, then scoop the avocado flesh into a medium bowl.
Mash the avocado with a large fork or potato masher. Stir in the garlic and about ½ tsp salt, plus the rest of the ingredients. Before chopping and adding the white onion, rinse it first under cold water, then shake well to rid it of excess moisture before adding to the avocado. (This reduces the risk of having the onion flavor overwhelm the guacamole). Taste and season with additional salt, if necessary.
If not using immediately, cover with plastic wrap pressed directly on the surface of the guacamole and refrigerate – preferably no more than a few hours.
Replace the lime juice with (or, for extra tangy guacamole, add along with the lime juice) about ½ cup homemade tomatillo salsa – perfect as a topping or a dip, especially when you need to make the guacamole ahead (the additional acid from the tomatillos helps keep the guacamole greener longer).
Avocado sauce: For a tangy sauce to drizzle over raw (or blanched) vegetables or on tacos, tostadas and the like, follow the above variation, increasing the tomatillo salsa to 1 cup; puree everything in a blender. If the sauce is too thick to drizzle, thin with additional tomatillo salsa. A little heavy cream, sour cream or crème Fraiche can be added for wonderful richness.