The simmering liquid is packed with flavor, which transfers nicely to the shrimp.
Bring first 10 ingredients and 4 qt. water to a boil in a large Dutch oven over medium-high heat. Reduce heat to medium-low; cover and simmer 20 minutes.
Add shrimp to Dutch oven. Increase heat to high, and return to a simmer. Add Spanish olives. Remove from heat, and cover with a tight-fitting lid. Let stand 5 minutes.
Drain shrimp and olives, discarding remaining solids. Place shrimp-and-olive mixture in a jelly-roll pan, and sprinkle with Shrimp Spice Mix. Serve immediately with cocktail sauces and lemon wedges, or chill 15 to 20 minutes or until cold.