Grate the ginger on the large holes of a cheese grater (a microplane or ginger grater will also work) or puree it in a food processor. Place the grated or pureed ginger in a cheesecloth or a thin linen towel and squeeze out the juice.
Cabbage can be shredded by cutting it into quarters, cutting out the core, and then, while the leaves are still together in layers, slicing thinly across them.
Slice the apples or Asian pear, if using, and then cut into thin strips and sprinkle some of the lime juice over them(to prevent browning). If using jicama, peel, slice and chop into thin strips.
In a medium skillet or saute pan, toast the sesame seeds over medium heat for about 3 minutes, stirring constantly until just golden and fragrant.
If using whole cumin seeds rather than already ground cumin, toast them over medium heat for about 3 minutes as well using the same skillet or pan, just until fragrant and then grind in a coffee/spice grinder.
To assemble the coleslaw:
In a large bowl, combine the cabbage, olive oil, cumin, and cayenne pepper, ginger and lime juice, and avocado, hand mixing to mash up some of the avocado pieces and coat the leaves. Add salt to taste.
Add in the cilantro, fruit, and sesame seeds, tossing well to disperse ingredients evenly in the coleslaw. Serve.