In a medium skillet, set over medium-low heat and add the butter and oil. Once the butter dissolves, stir in the onion and jalapeno. Let them cook, stirring occasionally, until the onion has softened. Its color will become translucent and the edges will begin to turn light brown, about 12 to 15 minutes. Incorporate the cilantro leaves and mix them in with the onions and jalapeno. Once the cilantro has wilted, 30 seconds to a minute later, turn off the heat.
Place the peeled and seeded avocados in the blender or food processor along with the cooked onion, jalapeno, cilantro, chicken broth, lime or lima juice and salt. Puree until smooth, taste for salt and add more if need be.
You may serve bowls garnished with tortilla crisps and cheese, or let your guests garnish to their liking.