Preheat the oven to 350 degrees.
In a microwave safe bowl, add the vegetable oil, celery, onion, thyme, sage, rosemary, oregano, salt and pepper. Cook until onions are translucent about 8 minutes. Stirring occasionally about every 1-2 minutes of cook time.
In a large bowl, add the cornbread and gluten-free bread. Stir in the cooked vegetables, melted butter, and chicken stock. Stir until thoroughly mixed. Taste the dressing and add salt and pepper as needed.
The dressing will be wet. This liquid is important during baking to keep the dressing from drying out.
Stir in the eggs. Transfer the dressing to an 8x10 casserole dish.
Bake for 60 minutes until the edges and top begin to brown.
Use a spook or fork to toss the dressing to make it look fluffy on top.
Garnish with parsley and serve.