2 to 4 pigeons, plucked and dressed 1/4 cup melted butter or olive oil Salt and black pepper 2 large carrots, peeled and cut into chunks 4 to 6 Jerusalem artichokes, cut into chunks 2 parsnips, peeled and cut into chunks 2 to 4 salsify roots, scrubbed and cut into 2-inch lengths (optional) 1 or 2 roots of Hamburg or root parsley, cut into chunks (optional) 3 tablespoons chopped parsley Beer…