À la béarnaise is a French cooking term that usually means with béarnaise sauce.
It can also mean something prepared in the cooking style of the region of Béarn. This can mean with ham from the area, such as jambon de Bayonne, or with tarragon, capers or a splash of vinegar.
Pot-Au-Feu à la béarnaise
This dish consists of a whole chicken filled with a stuffing made from minced garlic, minced parsley, minced shallots, the chopped livers from the chicken, chopped Bayonne ham and sausagemeat (or ground fresh pork.)
Béarn is the former name for a region in the Pyrenees mountains of France. Now the area is roughly occupied by the département of Pyrénées-Atlantiques.