Make the vinaigrette. Put the lemon juice, shallot, mustard, salt, sugar and mint in a blender and pulse briefly to combine. With the motor running, drizzle in the olive oil until it is well combined.
Using a mandolin, shave the fennel into 1/8 inch slices starting from the bottom of the bulb. Don’t worry about coring the fennel bulb, it’s unnecessary. If you don’t have a mandoline, slice the bulb as thin as you can. Chop some of the fennel fronds as well to toss in with the salad.
Toss with the fennel and marinate for at least an hour. Serve this salad either cold or at room temperature.