Small, firm lentils such as le Puy or beluga taste best in this dish. If you can’t find those, use small green lentils instead. They will be softer but still taste good. Don’t substitute red, brown or yellow lentils; they soften too much to work in this salad.
Pick the fronds off the fennel and reserve for garnish. Thinly slice the stalks and reserve the bulbs.
Combine the lentils, celery, onion, leeks, carrots, sliced fennel and 1 tablespoon salt in a large saucepan. Add enough cold water to cover by 2 inches. Bring to a boil over medium-high heat, then reduce the heat to medium-low and cook, stirring occasionally, until the lentils are just tender, about 45 minutes. If the water absorbs fully before the lentils are cooked through, add more.
Drain the lentils if needed, then transfer to a large bowl and add the vinegar, oil, mustard and dill. Fold until evenly coated, then season to taste with salt and pepper. Let sit for at least 10 minutes.
Halve the fennel bulbs, core and thinly slice. Scatter over the salad, along with the reserved fennel fronds. Drizzle with olive oil, sprinkle with salt and pepper, and serve.
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