Place the cookies in a resealable plastic bag and bash them with a rolling pin or use a serrated knife to chop the cookies unevenly. You want some cookie powder, some cookie crumbs, and some small cookie chunks. Stir the cookie powder, crumbs, and chunks into the crème fraîche and season with salt and pepper.
Pat the chicken breasts dry and slice them crosswise into strips about a scant inch wide.
Place a large skillet, preferably nonstick, over medium-high heat and add 1 tablespoon of the butter or oil. Add the chicken strips and sauté, adding more butter or oil if necessary, until the chicken is lightly colored on all sides and almost cooked through, about 7 minutes.
Season the chicken with salt and pepper. Add the cookie mixture to the pan. Bring to a boil and cook for another minute, stirring constantly, until the chicken is coated and completely cooked and the cookies seem to have melded into the sauce. Taste for salt and pepper, and serve as soon as it’s ready.