If using whole chicken breasts, slice each in half so you have four cutlets. Season the chicken cutlets liberally on both sides with salt and pepper. Set aside.

Slice shallots and set aside.

Mince fresh tarragon and set aside.

Chop fresh parsley and set aside.

Melt the butter and olive oil together in a large saucepan over medium-high heat.

Add the chicken cutlets to the pan and sear until golden brown on one side, 4-5 minutes. Flip the cutlets over and sear the other side, 1-2 minutes. Add 1 tablespoon of white wine to the pan, cover, and poach chicken, 5-6 minutes. If the pan gets too dry at any point, add the 2nd tablespoon of wine to create more steam.

Once chicken is cooked through, remove from pan onto a plate; keep warm.

Turn the heat down to medium and add the sliced shallots to the pan. Sautee until softened and lightly browned.

Add the ¼ cup white wine and deglaze the pan. Cook down so the wine reduces slightly but there is still some liquid in the pan, about 4-5 minutes. Add the minced tarragon and stir into the liquid.

Slowly stream in the heavy cream into the pan, stirring slowly but constantly. Let the mixture come to a boil, then reduce the heat to low and let it simmer for a few minutes, stirring occasionally. Taste and add more salt and pepper if you like.

Once sauce has thickened, add the chicken cutlets back to the pan. Turn the cutlets several times until they are warmed through and coated with sauce.

Serve the cutlets with a generous helping of sauce and a sprinkle of chopped parsley.