Cornbread with cookies

12 tablespoons butter (1 1/2 sticks) 2 cups finely-chopped yellow onions 3 tart apples , cored and chunked, but not peeled (Jonathan, Winesap or Granny Smith)[...]

1 1/2 cups pecans 6 tablespoons unsalted butter 5 cups cornbread, crumbled 5 shallots , finely chopped 1 celery rib , diced, into 1/4-inch pieces 10 ounces[...]