Preheat the oven to 400 degrees and grease two 9x9 baking dishes.
Make 2 flax eggs by combining flax meal and water. Set aside for 5 minutes to thicken.
Combine cornbread mix, flax eggs and almond milk in a bowl. Whisk together until smooth. Add cornbread mixture to the prepared baking dish and bake for 20-25 minutes, or until the center is cooked through. When cornbread is done, set aside to cool, uncovered, for 30-60 minutes.
Decrease oven heat to 375 degrees.
Add butter to a pan over medium heat. Once the butter is melted, add the onion and celery. Cook until vegetables start to become tender - approx. 5 minutes. Add the broth, fresh parsley, Italian seasoning, sage, thyme, salt and pepper to the vegetables and cook for an additional 1-2 minutes.
Slice cornbread into 1 inch squares and place in a bowl. Ladle broth mixture over cornbread until it reaches your desired consistency (see notes). Stir to combine - making sure not to over-mix.
Add mixture to a baking dish and top with dried parsley. Bake uncovered for 20-30 minutes, or until cooked through and the top begins to brown. Remove from oven and serve.