"In the style of Bordelais or Bordeaux." There are no hard and fast rules. It generally implies a sauce of shallots, wine (red or white) butter, tarragon and bone marrow and cooked with cep mushrooms. It can also mean simply cooked in wine (e.g. pêches à la bordelaise). Alternatively, it could also be a garnish of finely diced vegetables and sometimes ham or a garnish for poultry of artichokes and potatoes. Of fish and shellfish, it might mean cooked in wine with vegetables and herbs.
"In the style of the butcher." A dish prepared or garnished with bone marrow. This also refers to veal cutlets marinated in oil with seasoning and parsley, grilled and served with fresh vegetables.
"In the style of the baker." Baked or braised in the oven, often describing lamb dishes with onions and potatoes or chicken or fish. Before every household had an oven such dishes were often brought to the baker to be cooked after the bread was finished. It is a convenient way of baking multiple ingredients in one container.
"In the style of Boulogne-sur-Mer" or Boulogne-sur-Seine or of the Boulonnais area of Pas-de-Calais.
"In the style of the flower seller." A garnish for steaks and chops of mixed vegetables, carefully cut and arranged in bouquets. Alternatively it is a garnish for large joints of meat of artichoke hearts stuffed with balls of carrot and turnip, diced French beans, peas and cauliflower florets with hollandaise sauce and small château potatoes.
"In the style of Bourg-en-Bresse." Plain, sustaining cooking, often consisting of braised meat or poultry with onions, potatoes and chopped carrots.