Prepare the lemon confit: Cut the lemons in half and squeeze the juice (reserve it for the vinaigrette). Boil enough water to cover the lemon halves; add them to the pot with bay leaves, peppercorns and olive oil; cook at a moderate boil until they are tender. Let cool and remove all the remaining pulp. Scrape the white pith with a knife until it is all removed and you have clean lemon peel. Shred it into irregular pieces with your hands and store in an airtight container covered with olive oil. (To make a 9-ounce ball of confit, use 6 medium lemons.) It lasts for months in the refrigerator when well covered with olive oil.
While the lemons are cooking, wash the asparagus, pears and fennel. Break off the bases of the asparagus spears and then cut them into short pieces, length-wise, about three per stem. Place a pot of salted water on the stove and blanch the asparagus for a few seconds. Then transfer them to a bowl of cold water to stop the cooking process, remove them, and pat dry with paper towels.
Shave the fennel into thin slices and reserve in a bowl of cold water to prevent it from oxidizing.
Toast the pistachios in a low-temperature oven until crunchy and dry. Let them cool, then break them into pieces. Reserve.
Remove the leaves from the basil and mint and reserve for plating later.
Make the avocado cream: Juice the lemon into a bowl. Cut open one avocado at a time, remove the pit and spoon out the flesh immediately into the lemon juice. Add salt and pepper to taste, then purée in a blender and reserve.
Make the lemon vinaigretteand reserve.
To assemble the dish: In a bowl, place the fennel, basil and mint leaves, add salt, pepper, vinaigrette and reserve. Spread some avocado cream on a plate as the base. Arrange thin slices of pear in a flower pattern over the avocado cream and arrange the asparagus on top of them. Add the fennel salad on top, and, finally, the toasted pistachios.