Bring the vinegar and vermouth to a low simmer. Add the shallots and season with salt and pepper. Simmer to cook the shallots and reduce by half, 2-3 minutes.
Remove the pan from the heat and whisk in 4 tablespoons of butter until fully incorporated. Return the pan to low heat and whisk in the remainder of the butter, one piece at a time. Once the sauce is complete, add the lemon juice and dill. Serve hot.
To reheat, add a splash of water and whisk over low heat.