Put the tomatillos, jalapeno peppers, and the onion in a pot, covered with water. Boil them until they change color, about 5 to 7 minutes.
Meanwhile, cut the avocados in half and remove the pit. Scoop the avocado into the blender cup. Add the cilantro, garlic, half of the lime juice, garlic, and salt and pepper and purée.
Once the tomatillos, jalapenos, and onions are ready, add them also to the blender.
Finally add the olive oil, salt and pepper to taste.
Blend everything together until you make a smooth purée.
Now taste it and you can add the rest of the lime juice if you like or save it. You can also add more olive oil if you wish, but if you want to make it more liquid without the use of the oil, add more tomatillos until you reach the texture desired.
Serve warm or cold with chips, seafood, chicken or as salad dressing or topping on tacos.