In a foil-lined 15x10x1-in. baking pan, place the carrots, onion, yellow pepper and beet; drizzle with oil. Sprinkle with salt, pepper, cumin, cinnamon, ginger and allspice; toss to coat. Bake, uncovered, at 425° for 20-25 minutes or until tender, stirring once.
Meanwhile, make a slit down the outer curve of each shrimp, starting with the tail; press lightly to flatten. In three separate shallow bowls, place the flour, egg whites and coconut. Coat the shrimp with flour, dip into egg whites, then coat with coconut.
In an electric skillet or deep-fat fryer, heat oil to 375°. Fry shrimp, a few at a time, for 1 to 1-1/2 minutes on each side or until golden brown. Drain on paper towels.
In a microwave, heat the preserves, vinegar, butter and cayenne until preserves and butter are melted. Stir until smooth; drizzle over vegetable mixture and toss to coat.
Place 1/2 cup vegetable mixture on each lettuce leaf; top with shrimp and goat cheese. Fold lettuce over filling.