Trim outer leaves of artichokes all the way to the heart. Cook artichoke hearts in simmering water with lemon juice for approximately 7 to 8 minutes. Cool down in an ice water bath, and then cut into small sections.
Peel and cook asparagus for 1 minute in simmering water. Cool down in an ice water bath to keep green. Cut each spear into 3 pieces, on the bias.
Trim and snip green beans. Cook in boiling water for 2 minutes. Cool down in an iced water bath to keep green.
Clean and trim fennel. Cut out center part, and then cook in boiling water for about 40 minutes, or until tender. Cool down in an iced water bath. Cut into even wedges.
Slice fresh summer truffle very finely with a sharp knife, and set aside. In a small salad bowl, mix the shallots, olive and truffle oils, sherry vinegar, and salt and pepper, to taste. Set dressing aside.
Preheat a grill or grill pan to medium-high. Season halibut with salt and pepper, and grill on both sides until cooked through (fish should be opaque in the center).
On 4 large dinner plates, arrange baby lettuce, artichokes, asparagus, green beans, and fennel. Place halibut in the center on top, dribble with vinaigrette, and garnish with fresh summer truffle slices.
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