Combine first 5 ingredients in a large bowl. Stir in milk, eggs, and oil. Pour batter into a lightly greased 13- x 9-inch pan and bake at 425° for 20 to 25 minutes or until golden. Let cool in pan; finely crumble into a very large bowl.
Brown sausage in a large skillet, in batches if necessary, stirring until it crumbles and is no longer pink; drain, reserving 3 tablespoons drippings. Return reserved drippings and sausage to skillet, and stir in onion and next 2 ingredients. Cook over medium heat 7 minutes or until tender, stirring often. Add sausage and vegetables to cornbread in bowl, and stir well. Pour chicken broth over cornbread mixture; stir well. (Mixture will be wet.)
Spoon dressing into a lightly greased roasting pan. Bake, uncovered, at 350° for 1 hour or until set and browned.
If you like your dressing a little more firm, reduce the amount of broth by 1/2 cup.
I took this to our family Thanksgiving potluck this year. I was told to not come back for future Thanksgivings without this dressing! Many, many compliments on this and I'm making it again for Christmas!