You will have twice as much of the pesto as you need. You can cut the pesto amount in half, but I encourage you to make the full recipe. It will disappear quickly on bread, toast, or baked potatoes.
This is salad is even better if you use your finest olive oil.
Prepare the grill and let it burn down to medium-hot coals. Squeeze the lemon juice into a nonreactive bowl large enough to hold the avocados in a single layer. Halve the avocados, discard the pits, and scoop out the flesh in one piece with a rounded spoon. Immediately toss the avocados with the lemon juice to prevent discoloration.
Using a mandoline or sharp chef's knife, thinly slice the onion. Separate the onion into rings and place in another bowl. Pour some of the lemon juice from the avocados over the onions and season with salt and pepper. Toss well and set aside. Cut the tomatoes lengthwise into thin wedges, season with salt and pepper, and reserve.
Remove the avocados from the lemon juice and set the bowl aside. Season the avocados on all sides with salt and pepper and drizzle very lightly with about 1 tablespoon of the olive oil. Too much and the oil might cause flare-ups.
Grill the avocados, cut side down, until the outside edge looks a little dry and browned, about 2 minutes. Turn onto the rounded side and cook for another 2 minutes. Since so little area is exposed to the heat, this is just to soften, not cook, the avocados. If the avocados were very firm, leave on another minute. Do not turn too often or they may disintegrate. Return the grilled avocados to the bowl with the lemon juice. Spoon the lemon juice over them and set aside until cool enough to handle, then cut into thin wedges.
Place several onion rings in the center of each salad plate. Arrange the avocados on opposite sides and the tomatoes on the remaining two sides. Drizzle each salad with about 1-1/2 teaspoons olive oil and 1 teaspoon pesto. Season again with salt and pepper to taste and give each salad a coarse grating of cheese. Scatter the pine nuts on top, if using, and serve immediately.
Chef's Note: These directions are for a plated salad. These same ingredients can be used to make a layered salad in a bowl. Cut the avocados and tomatoes into large, equal-size pieces, layer in a bowl with the onion rings, and drizzle with the lemon juice, olive oil and pesto as you layer.
