1. Make the shrimp: In a medium saucepan set over medium-high heat, bring the water, ginger, garlic and lemongrass to a simmer. Squeeze in the juice from two lemon halves and add the squeezed halves to the pot. Reduce the heat to medium-low and let the mixture infuse at a bare simmer for 20 minutes.

2. Meanwhile, make the cocktail sauce: In a medium bowl, stir together the kimchi juice, tomato sauce, ketchup, chile-garlic sauce, lemon zest and juice and salt. Place the grated ginger in a teaspoon and hold over the bowl while pressing on the ginger to extract the ginger juice, pouring the ginger juice into the bowl (discard the pulp). Stir to combine, cover with plastic wrap and refrigerate to chill.

3. Drop the shrimp into the saucepan of simmering water and cook until pink and cooked through, 3 to 4 minutes, depending on the size of the shrimp (to test a shrimp, use a slotted spoon to remove it from the saucepan and slice through it; it should be opaque all the way through). Turn off the heat and drain the shrimp through a colander, then use tongs to transfer the shrimp to a rimmed baking sheet to cool. Place the shrimp in the refrigerator to cool completely, at least 1 hour or overnight.

4. Once the shrimp are cold, use a paring knife to make a shallow slit down the curved back of the shrimp and remove the vein (if there is one). Peel off the shell, leaving the tail attached. Serve the chilled shrimp with kimchi cocktail sauce and lemon wedges.