To prepare the beurre blanc, first mince the shallots. Crush the peppercorns using a small, heavy fry pan or mallet. Cut the cold butter into tablespoon-size pieces and set aside. Gather the vermouth and white wine vinegar.
Place a small saucepan over medium heat. Add the shallots, vermouth, white wine vinegar and crushed pink peppercorns. Bring to a simmer and reduce the liquid by about two-thirds until it reaches a syrupy consistency.
Turn the heat to the lowest setting and whisk in the cold butter one piece at a time to slowly form the emulsion.
Once all of the butter has been incorporated, season with salt and pepper. You may want to add a few more drops of lemon juice to brighten the flavor of the sauce, if needed.
Monitor the sauce closely while you cook the fish. Keep the sauce warm to the touch and whisk often to prevent it from splitting. You may need to turn the heat off and on to keep it at the correct temperature. The heat does not always need to be on, as the residual heat from the pan will keep it warm.