Step 1Puree the garlic and salt using a mortar and pestle or in a blender. Add the walnut halves and grind to a thick paste. Add the vinegar and puree a little more. The paste will loosen and smooth out.
Step 2Beat in olive oil just until the paste holds its consistency. When you see oil start to separate, stop.
Step 3Stir in the basil leaves and season to taste with more salt if necessary. The pesto can be prepared up to 2 hours before serving. Stir vigorously before serving.
Step 1Cut away the branches from the fennel. Chop and reserve about 1 tablespoon of fronds. Cut the fennel heads in quarters lengthwise and remove the solid core that runs down the center of each quarter. Slice the fennel horizontally as thin as possible using a heavy knife. Place the sliced fennel in a large work bowl.
Step 2Whisk together the lemon juice and one-fourth cup olive oil in a small bowl. Season to taste with salt. Pour over the sliced fennel and the reserved fronds, toss well and set aside to marinate while you prepare the rest of the dish. (The recipe can be prepared to this point up to 1 day ahead; refrigerate the fennel.)
Step 3Preheat the broiler. Pat the sardines dry on both sides. Season the meat side of the sardines with salt and arrange the fish skin-side up on a broiler pan. Drizzle lightly with a little olive oil and rub with your fingers to distribute it over the fish. Season the skin side with salt and broil until the skin is well browned and the fish is bubbling hot, 4 to 6 minutes.
Step 4Arrange the fennel in a low mound on the serving platter. Arrange the sardines over top. Spoon dollops of walnut pesto on top; serve immediately.