Grab a large stock pot or Dutch oven and set over medium heat. Add oil and let it get hot. Once hot, add flour and whisk together until smooth. Continue whisking to cook the roux for about 10 minutes or until it turns a little darker than the color of peanut butter.
Add the onion and whisk together with the roux. Cook until the onions soften, about 6 minutes. Add the garlic and cook for 1 more minute, making sure not to burn it. Add the stock about 1 cup at a time, whisking after each addition and letting the mixture thicken up before adding the next cup. Bring the mixture to a gentle boil.
Add bay leaves, pepper, cayenne, thyme leaves, and 4 teaspoons of salt. Stir together and then reduce heat to low so that it's just barely simmering. Cook for about 35 minutes, stirring occasionally so that the bottom does not burn.
Add the diced potatoes to the stew. Cook uncovered until the potatoes are tender, about 30 more minutes. Season the shrimp with remaining ½ teaspoon of salt. Add shrimp to the stew, along with green onion and parsley. Cook until the shrimp are cooked and pink, about 4 minutes. Remove the bay leaves and serve with steamed white rice.