Bring a large pot of salted water to a boil.
Add the shrimp to the boiling water and cook for 2-3 minutes until pink and opaque.
Remove the shrimp from the pot and immediately place them in an ice bath to stop cooking.
Once cold, drain the shrimp and pat dry with paper towels.
Prepare the cocktail sauce by mixing ketchup with horseradish to taste.
Arrange the shrimp in serving glasses or bowls.
Add a generous dollop of cocktail sauce on top of the shrimp.
Garnish with lemon wedges and parsley.
Serve chilled or at room temperature.
Enjoy your fresh shrimp cocktail with a splash of hot sauce if desired.