Grease the interior of the deep casserole pan with the butter and set aside. 

Set a medium sauté pan over medium heat and add the bacon.  Cook until most of the fat has rendered and the bacon is crisp and golden brown.  Using a slotted spoon, remove the bacon from the pan and set aside. Add the corn to the pan.  Cook the corn, stirring often until the corn is lightly caramelized and softened, about 10 minutes.  Add the onion, bell pepper and celery and cook until softened, about 5 minutes.  Add the garlic and thyme to the pan and remove from the heat.  Stir to incorporate all of the ingredients and transfer to a large bowl.  Add the milk, cream and eggs to the bowl and whisk well to combine.  Season with the salt, Essence, and Cayenne pepper.  Fold in the bread and Monterey Jack cheese and mix until the bread has absorbed most of the liquid. 

Pour the pudding mixture into the buttered bucket pan.  Place the pan in the basket of the Air Fryer, then into the drawer and close it. Set the temperature to 320 degrees Fahrenheit and the timer for 30 minutes.  Once the timer goes off, open the door to the Air Fryer and sprinkle the Parmesan cheese evenly over top of the corn pudding. Close the drawer and set the timer for another 30 minutes.  When the timer goes off, remove the corn pudding from the Air Fryer and allow to cool for at least 20 minutes before serving.