Season the pork chops on both sides and brown in a little olive oil in a large dutch oven.
Remove the browned chops to a plate and cover.
Saute the onions, garlic, celery, carrots and mushrooms until the carrots soften, adding a little more olive oil if necessary.
Sprinkle the flour over the veggies and stir well to combine. Cook for a couple minutes to allow the flour to cook.
Add the broth a cup at a time, stirring well and allowing the contents to come to temperature before adding more. Season with salt, pepper and thyme. The sauce should be gravy like. (Leave some of the broth in reserve).
Stir in the rice.
Bring the contents to a nice bubble, then reduce the heat and put the lid on the dutch oven.
Add any additional vegetables as the rice cooks. Stir well to combine and add the reserved broth as needed.
Return the pork chops to the dutch oven along with any accumulated juices so they can finish cooking (the rice was almost ready when I added the thin ones we used). Just lay them on top of the rice. Replace the lid and allow the meat to cook through.