Melt 1 tablespoon of the butter in a small saucepan or skillet over medium-low heat. Add the shallots and cook, stirring, until it is softened but not browned, about 1 minute. Add the lemon zest and juice and bring the mixture to a simmer. Vigorously whisk in the remaining butter, 1 tablespoon at a time, allowing each addition to melt before adding the next. The sauce should be slightly thickened and the butter emulsified. Stir in the dill and season with the salt and pepper to taste.