Begin by preheating oven to 400 degrees. Prepare two sheet pans with parchment paper. Add diced cornbread to one sheet pan and diced biscuits to the other. Toast in the oven until golden brown, 8-10 minutes, tossing once midway through. Set aside and leave oven on.
To a large saute pan over medium heat, add butter and avocado oil followed by onion, celery, red and green bell pepper. Begin to saute until vegetables are translucent, 8-10 minutes. Stir in herbs, seasonings, garlic and corn and saute another 3-5 minutes, turning down heat if needed. When vegetables are tender and caramelized, stir in ham and set aside off the heat.
To make custard, add all ingredients to a medium bowl or blender. With an immersion blender, blend well until incorporated or pulse with a blender until incorporated.
To a large bowl, add toasted biscuit and cornbread croutons and sautéed vegetable and ham mixture. Mix well with a spatula. With a 1-cup measurement, slowly add a cup of custard at a time, stirring uniformly. Add all custard in batches until dressing is incorporated and moistened.
Transfer the dressing too a greased 9x11 casserole dish. Add small cubes of butter uniformly atop and transfer to the middle rack of the heated oven.
Bake dressing for 25-35 minutes until top is golden brown and bubbling. Serve immediately and enjoy.