While a mandoline may seem "chef-y," it's actually a great tool for making perfectly thin slices of potato, beet, fennel and more. It is the most dangerous tool in the kitchen, but I'll show you some ways to use it safely and easily.
Put the soaked chickpeas in a medium saucepan along with about three quarts of water, and set over medium-high heat. Bring to a gentle simmer, and cook 1–2 hours, depending on the age of the chickpeas.
Tie the celery, carrot, onion, lemon peel, 1 garlic clove, and rosemary in a piece of cheesecloth and add it to the pot. Season the beans generously with salt and add 1/4 cup of olive oil.
Once the beans are cooked, remove from heat, drain (reserving the liquid, if you like), and let cool completely. Combine lemon juice, a pinch of salt, and remaining olive oil in a small mixing bowl. Drizzle a couple of tablespoons of this dressing over the chickpeas. Add remaining garlic clove to chickpeas and toss to coat. Smash the basil sprigs with the side of a knife and add to the chickpeas. Add a pinch of chili flakes, and let the chickpeas marinate while you prepare the other ingredients.
Trim the fennel bulb, saving the fronds for a garnish. Halve the bulb lengthwise, and shave both halves into paper-thin slices with a mandoline. Quarter the Asian pear, discard the core, and shave into paper-thin slices. Combine with the fennel.
Assembly: Remove basil and garlic from the chickpeas, and discard. Combine chickpeas with shaved fennel and pear and remaining dressing. Toss gently to coat. Taste and season with salt, if desired. Garnish the salad with coarsely chopped fennel fronds. Serve immediately.