Pour the sauce into the shallot mixture. Add 1 1/2 teaspoons of the tarragon, season with black pepper, and stir to combine. Taste and season with more kosher salt, black pepper, or lemon juice as needed. The sauce should be thick enough to coat a spoon, but thin enough to drizzle from the spoon. If it is too thick, thin it out with water 1/2 teaspoon water at a time. Garnish with the remaining 1/2 teaspoon tarragon and serve immediately.