Place onion, chile, half of cilantro leaves, and a large pinch of salt in a molcajete or mortar and pestle. Pound into a fine paste. Alternatively, combine onion, chile, half of cilantro, salt, and half of lime juice in a food processor or blender and process, scraping down sides as necessary, until smooth paste is formed.
Split each avocado in half, discard pits, and spoon out flesh into the molcajete or mortar and pestle (if large enough), or combine with the onion-chile purée in a medium mixing bowl. Roughly mash with the pestle or a stiff whisk.
Stir in remaining cilantro leaves, then season with lime juice and salt to taste. Serve immediately with warm tortilla chips or as desired.
