Preheat the oven to 350°F.

Cut the fennel bulb in half lengthwise, then cut each half into 3 wedges. Add to a small baking dish, drizzle with olive oil, then sprinkle with a big pinch of kosher salt. Pour in 1/4 cup water, cover tightly with foil, and bake until fork tender (when an inserted fork meets no resistance, about 1 hour). Uncover and let cool completely.

Transfer the fennel to a cutting board, and remove the core from each wedge. Discard cores. Also remove any outer layers that are more fibrous than the inner layers. Finely chop the remaining fennel. You want this to be as fine as possible, so the fennel gets well-distributed into the guacamole. Set aside half of the chopped fennel for the guacamole, and store the remaining half in the refrigerator for another use.

Add apple and lime juice to a small bowl, tossing to combine. Set aside while you prepare the avocado.

Slice open each avocado lengthwise, and carefully remove the pit. Using a sharp knife, make diagonal cuts down the avocado. You want to cut just the flesh, not the skin. Turn the avocado and make another set of diagonal cuts, forming a cross-hatch pattern. Scoop the flesh into a large bowl. The flesh should come out in a nice dice.

Add the apple (with lime juice), cilantro, jalapeno, 1 teaspoon of kosher salt and reserved fennel to the bowl with the avocado. Using two forks, roughly mash the ingredients together. Add additional salt, lime juice and cilantro to taste. Serve with tortilla chips.