In a large saucepan bring 6 cups water to boiling. Add snow peas, haricots verts, and asparagus. Return to boiling; reduce heat. Boil gently, uncovered, for 2 minutes. Using a slotted spoon, immediately remove vegetables from water; plunge vegetables into a large bowl half-filled with ice water. Let stand for 10 minutes. Drain vegetables well; pat dry with paper towels. Transfer vegetables to the large bowl.
In a small bowl, combine salad dressing and Jamaican jerk seasoning; pour over vegetables, tossing to coat. Transfer vegetables to a serving platter or bowl and sprinkle with sesame seeds.