The combined flavors of lemon, vinegar, and anchovies give depth to the herbs.
Place the shallots in a mortar. Add the salt, and, using the pestle, pound until a paste forms. (If a mortar is unavailable, place the shallots on a cutting board, and sprinkle the salt over the top. Using the side of a chef's knife, crush the shallots against the board. Continue crushing until a paste forms.) Add the pepper and the anchovies, if using. Work mixture, with either pestle or knife, until a paste forms again. Transfer the mixture to a medium bowl.
Using a small whisk or a fork, mix the oil, the lemon juice, the lemon zest, and the vinegar into the shallot paste.
Using a large chef's knife, chop the herbs until medium-fine. Add herbs to the bowl with the shallot paste. Add the chives. Using a rubber spatula, gently combine ingredients. Serve sauce the same day.
The walnut oil can be replaced with canola oil. Also, the tarragon vinegar can be replaced with white-wine vinegar.