Barbara Lynch began her career as a Todd English protégé, then traveled around Italy learning how to make pasta from nonnas. Today she runs a Boston food empire notable for its breadth. There are restaurants: the lovely Italian-French No. 9 Park, the luxe Menton and counter spots Sportello and B&G Oysters. And there’s also Drink, one of America’s best cocktail bars; The Butcher Shop, which doubles as a wine bar; and Stir, a demo kitchen and cooking school. It’s hard to think of another American chef who focuses so hard and well on so many kinds of projects.