1/4 cup finely chopped shallot
1/2 stick butter cut into 1/2-inch cubes.divided
1/3 cup dry white wine
1 1/2 pounds chicken tenderloins, tendons removed, pounded thin
Salt and pepper to taste
2 tablespoons olive oil
1/4 cup chopped fresh tarragon
1 tablespoon finely chopped fresh flat-leaf parsley
2 teaspoons fresh lemon juice
Cook shallot in 1 tablespoon butter in a small heavy saucepan over moderate heat, stirring occasionally, until softened, about 2 minutes. Add wine and boil until most of liquid is evaporated, about 3 minutes. Set aside.
Pat prepared chicken dry and sprinkle all over with salt and pepper. Heat oil in a 12-inch heavy skillet over moderately high heat until hot but not smoking, then saute chicken in batches, turning over once, until golden and just cooked through. Transfer as cooked to a platter and keep warm, loosely covered with foil.
Return shallot mixture to moderately low heat and add remaining 3 tablespoons butter, 1 cube at a time, whisking until incorporated. Remove from heat and whisk in tarragon, parsley, and lemon juice. Spoon sauce over chicken.