Keep the green herb tops of the fennel bulbs. Slice the fennel bulbs as finely as possible lengthways so that each slice remains attached to the stalk. Place in a bowl of iced water with the lemon half to prevent discoloration.
Preheat a grill. Dry the fennel slices in a cloth and grill on both sides until they have char marks but remain al dente.
Place in a bowl and toss with t