Place large pot on stovetop over medium-low heat. Add 3 quarts cold water, 1 cup sliced white onion, 2 cloves garlic, 2-3 sprigs fresh tarragon, 1 tablespoon seafood seasoning , 1 teaspoon whole black peppercorns, and 1 large bay leaf to pot.
Squeeze juice from 2 medium lemon halves directly into pot, then add both lemon halves to pot. Stir ingredients together to incorporate, then simmer mixture 15 minutes, stirring occasionally.
After 15 minutes, increase heat under pot to high and bring water to rapid boil. While water comes to boil, fill large bowl with cold water and ice. Set aside.
Once water begins to boil rapidly, add 1 pound jumbo shrimp to pot. Cook shrimp approximately 2 to 4 minutes, just until shrimp are bright pink, opaque, and loosely curled into "C" shape.
When shrimp are fully cooked, immediately remove shrimp from pot with slotted spoon and submerge shrimp in ice bath to stop cooking.
Once all shrimp have been transferred to ice bath, discard remaining water and aromatics.