Add pickling spice and lemon juice to 1 qt. water, bring to boil.
Peel orange and supreme into sections. Squeeze remaining orange into water.
Turn water to simmer and add shrimp; cook until pink and just cooked through. Remove shrimp and chill completely. Remove tails from shrimp and cut each shrimp into fourths.
Peel avocado, remove pit, and dice. Add oranges and avocado to shrimp. Dress shrimp, orange, and avocado with ginger sesame vinaigrette; add basil, season to taste.
9. Place 1/2 c. shredded iceberg lettuce in each chilled Martini glass.
Remove core from tomato, cut in half, place cut side down; slice each half as thinly as possible.
Fan each half of tomato, place half of each into glass to garnish. Divide shrimp and avocado cocktail into each glass and serve chilled.