Squeeze the juice of one lime half over the flesh of the avocados to prevent oxidation. Brush cut-side of avocado halves, remaining lime halves, and both sides of the red onion slices with olive oil. Lightly season with salt and pepper.
Preheat grill over a medium-high flame. Oil grates, or line with a non-toxic, nonstick grill mat.*
Grill onions until soft and caramelized, about 5 minutes per side. Grill avocados and limes, cut-side down, until grill marks appear with a light char, about 5 minutes. Times may vary by grill. Remove to platter to cool.
When avocados are cool enough to handle, scoop flesh into a large bowl and mash to desired consistency (I like to leave my guacamole a little chunky). Chop grilled onions (you should have between 1/2 and 3/4 cup).
Stir chopped onions, garlic, cilantro, ground cumin, 1/2 tablespoon (1-1/2 teaspoons) extra virgin olive oil, 1 teaspoon kosher salt, and 1/2 teaspoon pepper into the mashed avocados.
Add 1-2 tablespoons grilled lime juice, to taste, and stir to combine. Cover and let stand at least 30 minutes for flavors to meld. Season to taste with additional salt and pepper.
Serve, with a drizzle of extra virgin olive oil and an additional pinch of cilantro, if desired.
When grilling directly on the grates (as opposed to a grill mat) I like to thread the onion slices on metal grilling skewers so that they don't fall apart when they're flipped.
Add a little heat:
I like to allow the smoky flavor of the grilled avocados and cumin shine through in this guacamole, without adding "heat." If you like your guacamole spicy, feel free to add some de-seeded, grilled, chopped jalepeño pepper or a few dashes of hot sauce to taste.