Mix ketchup, horseradish, lemon juice, vinegar, sugar, salt, pepper, smoked paprika, and hot sauce in a bowl. Taste it before anything else happens—this moment tells you if your horseradish is fresher than mine or needs adjustment. I always taste because bottled horseradish strengths vary wildly between brands.

Stir in the fresh dill just before serving the sauce, not before. This keeps the dill green and bright instead of darkening into the background, which happens when it sits in liquid for hours.

Pat the shrimp completely dry with paper towels—this step determines whether they sear or steam. Wet shrimp never crisp properly, and I learned this the hard way during a dinner party disaster three years ago.

Heat unsalted butter in a large skillet over medium-high heat until it foams. Cook shrimp for 2-3 minutes per side, watching for the color change from gray to opaque pink. Overcooked shrimp ruins everything, so set a timer because it happens faster than you expect.

Remove shrimp from heat immediately when the thickest part turns opaque. They keep cooking in their own heat, so pulling them early gives you that tender bite instead of the rubbery texture that makes people push them around their plate.

Let shrimp cool for five minutes on a clean plate before serving with your sauce. This resting period prevents the heat from cooking them further and gives the flavors a moment to settle.

Arrange cooled shrimp around a small bowl of sauce, or serve them on toothpicks with sauce cups nearby. Either way, this shrimp cocktail party crowd presentation matters because people eat with their eyes first.