Chop ½ of the onion into four pieces and place in a food processor. Cut the stem off the jalapeno and deseed (optional - if you leave the seeds in, it will be hotter), and add to the food processor. Cut garlic into four pieces and add to food processor. Add cilantro, lime, salt, and cayenne pepper. Pulse until everything is chopped into small pieces. The goal is a fine chop, don't process it too much, or it will become minced. Combine the mixture with mashed avocados!