Preheat the oven to 400 degrees F. Spread enough of the rock salt across the bottom of a baking sheet to make an even layer (about half of the salt). Place in the oven to preheat for 30 to 45 minutes.

Place the rosemary sprigs across the hot salt, spacing evenly, and place 1 shrimp on top of each. Top the shrimp with the remaining salt to cover completely. Bake until the shrimp are pink and cooked through, about 10 minutes.

While the shrimp are cooking, make the dipping sauce. In a small saucepan, melt the butter over medium heat. Add the remaining ingredients and gently cook until aromatic, about 5 minutes. Remove from the heat and pour into a decorative bowl to serve warm.

To serve, remove the shrimp with tongs and place on a platter. (Alternatively, peel the shrimp before serving.) Serve the shrimp with the warm butter dipping sauce on the side.