Preheat oven to 400 F. In a large measuring cup, whisk together milk and vinegar. In a large bowl, whisk together flour, cornmeal, sugar, salt and baking powder.
Add in the milk mixture, eggs and vegetable oil. Mix until smooth. Pour cornbread mixture into a greased 9x13-inch baking dish. Bake for 30-35 minutes. Let cool slightly. Reduce oven temperature to 350 F.
When the cornbread is cool enough to handle, crumble it into a large bowl. Melt butter in a medium saucepan over medium heat. Add in the diced onion and celery and cook until softened.
Add the vegetable mixture with the crumbled cornbread along with the broth and poultry seasoning. Mix until combined.
Press the cornbread mixture into a large greased baking dish. Bake for 1 hour.
