Bring vinegar and vermouth to a low simmer. Add shallots and season with salt and pepper. Simmer to cook shallots and reduce by half, 2-3 minutes.
Remove pan from heat and whisk in 4 tablespoons of butter until fully incorporated. Return pan to low heat and whisk in remainder of butter, 1 piece at a time. Once sauce is complete, add lemon juice and dill. Serve hot.
To reheat, add splash of water and whisk over low heat.