Step 1To make the stuffing, combine 1 1/2 cups chopped sorrel, garlic, 1 tablespoon shallots, olive oil, one-half teaspoon salt and pepper to taste.
Step 2Wash the chicken breasts and pat dry. Make a pocket for the stuffing by loosening the skin from one side of each chicken breast, leaving it attached on the other side as much as possible. Spoon the sorrel mixture under the skin of each chicken breast. Season the chicken with salt and pepper to taste.
Step 3Heat 3 tablespoons butter over medium-high heat in a large skillet until the butter melts and foams. Arrange the chicken breasts skin-side-down in the pan. Cook until nicely browned, about 10 minutes, then turn the chicken over. Reduce the heat to medium-low and continue to cook until almost done, about 5 to 10 minutes longer.
Step 4Remove the chicken to a warm platter, cover with foil and let stand in a warm place while making the sauce.
Step 5Pour out all but 1 tablespoon drippings from the skillet. Add the remaining 1 tablespoon shallots and saute 1 to 2 minutes. Add the wine and stir to deglaze. Cook until the wine is reduced and syrupy-looking, about 3 minutes.
Step 6Add the remaining 2 cups chopped sorrel. Cook and stir until the sorrel is wilted and turns olive green, about 1 minute. Stir in the chicken broth. Bring to a simmer and cook about 5 minutes.
Step 7Add the cream, remaining three-fourths teaspoon salt and dash of pepper during the last minute of cooking. Pour the sauce into a blender and puree until smooth, then pour it back into the skillet. Add remaining 1 tablespoon butter a little at a time, swirling the pan, until the sauce is slightly thickened and shiny.
Step 8To serve, slice the chicken breasts and spoon the sauce over.