Combine half the onions, half the jalapeño, and half the cilantro in a mortar or food processor, season with about 1/2 tsp. salt, then pulse or grind into a smooth paste. Transfer to a medium bowl. Cut avocado in half lengthwise, then remove and discard pit. Make crosshatch incisions in avocado pulp with a paring knife. Scoop pulp out with a spoon, then combine with onion mixture. Mix well with a wooden spoon. Stir in remaining onions, jalapeño, and cilantro, then gently mix in tomatoes.

Season to taste with salt. Transfer to a serving bowl and serve with tortilla chips, if you like.