Combine the wine, bay leaf, fennel bulb, peppercorns, onion, salt, spent lemon half, and 6 cups cold water in a wide saucepan. Bring to a boil, then reduce the heat and simmer for 15 minutes — this is when the aromatics open up and actually flavor the liquid. Don't rush it.
2 cups dry white wine, 6 cups cold water, 1 bay leaf, 1 small fennel bulb, 1 tsp whole black peppercorns, 1 small yellow onion, 2 tsp kosher salt, 1 spent lemon half
Make the cocktail sauce. Stir together the ketchup, horseradish, Worcestershire, and Tabasco. Taste it — it should be punchy, savory, and have real heat. Refrigerate until ready to serve. Do not add the tarragon or lemon juice yet.
1 cup ketchup, 3 tbsp jarred horseradish, 1 tsp Worcestershire sauce, ½ tsp Tabasco
Bring the court-bouillon back to a rolling boil. Add the shrimp, working in batches if needed to avoid crowding. Poach for 2–3 minutes, watching closely. You're looking for a gentle C-curve and opaque pink flesh — the moment you see it, they're done. A tight curl means you've gone too far. Transfer immediately to the ice bath — this stops the cook instantly and is what gives you that clean, tender snap.
2 lbs jumbo shrimp
Leave the shrimp in the ice bath for 3 minutes, then transfer to a paper towel-lined sheet pan. Pat dry and refrigerate until fully chilled, at least 30 minutes. Cold shrimp on cold ice is non-negotiable.
Just before serving, stir the tarragon and lemon juice into the cocktail sauce. These go in at the last moment — tarragon wilts and lemon fades fast. Adjust salt. Arrange the shrimp over crushed ice, sauce alongside, and scatter the reserved fennel fronds over the top.
2 tbsp fresh tarragon leaves, 1 tbsp fresh lemon juice