Preheat the oven to 400 degrees F. Line a baking tray with parchment paper and set aside.
In a large bowl, add the peeled shrimp, garlic, salt, pepper and olive oil and mix to combine. Spread the shrimp out onto the baking tray in an even layer and so that they are not touching.
Roast the shrimp in the oven for 3-4 minutes per side. Once the shrimp have turned pink and are cooked through, remove them from the oven and let them cool completely.
To make the cocktail sauce, combine the ketchup, horseradish, Worcestershire sauce, hot sauce and lemon juice in a small bowl and mix to combine. Taste and adjust the seasoning if you would like by adding more ketchup (for sweetness), more horseradish or hot sauce (for spiciness) or lemon juice (for tartness).
Place the cocktail sauce in a decorative bowl and place on a large platter. Arrange the cooled shrimp on the platter and garnish with a bit of parsley and lemon wedges. Keep these shrimp chilled in the fridge until you are ready to serve them.
Note: Do not eat shrimp that has been left out at room temperature for over 2 hours. That will likely not be a problem as these will disappear so fast!