Prepare all of the ingredients. Preheat oven to 350deg.
In a large oven safe saute pan over medium-high heat, add butter for pork chops. Season pork chops on both sides with salt, pepper, garlic powder and tarragon. Cook for 2-3 minutes on each and remove from heat.
In the same pan, reduce heat to medium and add avocado oil and flour. Whish together and let cook for 3 minutes. Whisk in chicken stock, salt, garlic powder and rosemary. Cook 3 minutes then add milk and cheese. Continue stirring while cheese melts. Increase heat to medium-high and add rice. Continue to stir and bring to a boil. Let boil 3 minutes more than add pork chops back to pan in a single layer. Cover with oven safe lid (or aluminum foil if you don't have a lid). Place in oven and cook for 30 minutes.
Remove pan from heat. Working quickly, remove lid and sprinkle top with remaining cheese and tarragon. Replace lid and let rest for 10 minutes more.