1Cut the lemon in half and squeeze to measure 2 tablespoons of the juice. Transfer the squeezed lemon halves and any remaining lemon juice to a medium bowl and add about 4 cups of iced water.
2Trim o the stalks, fronds, and tough outer layer from the fennel. Trim the bottom of the bulb. Cut the bulb in half lengthwise. With the tip of a small sharp knife, dig out the solid core from the bottom of the bulb.
3 Discard the trimmings. Using a V-slicer or mandoline, cut the fennel into thin slices. Transfer the slices to the lemon water. Let stand to crisp for 15 to 20 minutes.
4Using the large holes on a box grater, press hard to shred the unpeeled apples down to the core, discarding the core and tough bits of skin. Drain the fennel well, discarding the ice, and dry the fennel by patting it with paper towels or in a salad spinner.
5Whisk the reserved lemon juice, vinegar, honey, and hot red pepper flakes in a medium bowl. Add the fennel, apples with any juices, and the cilantro and mix well, seasoning to taste with the salt and black pepper. Cover and refrigerate to blend the flavors for at least 1 hour. ( The slaw can be refrigerated for up to 1 day.) Let the slaw stand at room temperature for 15 minutes before serving.
TIP Some people can’t stand cilantro. This phenomenon seems to be genetic and not just personal. In that case, just leave it out. When I was growing up I remember seeing cilantro (coriandolo) in some markets, but my family never cooked with it. I had to get to LA to really appreciate the herb. If you wish, substitute at-leaf parsley or, if you like the mild licorice avor of fennel, use the nely chopped fennel fronds.