Step 1Cook the beet in boiling salted water until tender, about 40 minutes; trim and peel.
Step 2Cut it into quarters, and place it in a blender with shallots, vinegar, honey, water, and salt and pepper. Puree, then slowly add one-half cup oil until the mixture is smooth (covering the blender with a towel to prevent splatters). Makes three-fourths cup.
Step 1Boil the farro in a quart of salted water until al dente, about 30 minutes. Drain. Place the cooked farro in a bowl and dress it with 2 tablespoons of oil and salt and pepper. Set aside.
Step 2Combine celery leaves, and mixed carrot tops and chive pieces with 1 teaspoon of olive oil; set aside.
Step 3Tie a stick to each lobster tail to prevent curling. Place the lobsters head first in a large pot of boiling water. Return to a boil and cook for 5 minutes. Remove lobsters from the pot and cool to room temperature.
Step 4Place each lobster on its back and using a knife or shears, cut into the underside of the shell, catching and reserving juice. Reserve the green tomalley (liver). Remove meat from tail and slice it into medallions. Carefully remove meat from each large claw in one piece.
Step 5In a bowl, whisk the lobster juice, tomalley, chopped chives, 1 to 2 tablespoons of the remaining olive oil, lemon juice and salt to taste. Dress the lobster meat with this mixture.
Step 6To serve, put a ring mold (4-inch by 2-inch) on each plate. Layer salad by placing one-half cup of dressed farro in the bottom of each mold, then an equal number of medallions and claws, then an equal amount of the greens. Carefully remove the mold so the salad is presented in a stack. Drizzle the vinaigrette over the lobster and on the plate. (If you don't have ring molds, mound and layer the ingredients to create a neat stack.) Serve immediately.