Heat a small comal or heavy skillet over medium-high heat for a few minutes. Char the tomatillos, jalapeno pepper, wedge of white onion and clove of garlic on as many sides that will lay flat on the comal. Char to a deep mahogany. Remove to a plate as needed. Set aside.
Peel the charred skin from the jalapeno pepper using the back of a small knife, or with your fingers, wearing gloves if needed to protect your skin. Slice in half lengthwise to remove the seeds and any stringy membrane. Slice into thin, julienne strips. Taste for spicy-heat level to determine how much you will use in the salsa. About one-quarter to half of a jalapeno will suit most palates for heat tolerances.
Chop the avocado, tomatillos and onion into about half inch pieces and add to a small food processor or blender. Add the garlic, cilantro and lime juice, salt and pepper. Blitz to form a smooth consistency. (If you have a molcajete use it!)
Taste and add more jalapeno, salt and/or pepper as desired. Transfer to a serving bowl, cover and refrigerate if not serving immediately.The salsa will keep in the refrigerator for a couple of days if well covered.