Combine the rinsed rice, water, and 1/2 teaspoon kosher salt in a saucepan. Bring to a boil, cover, reduce to low, and cook for 15 minutes. Turn off the heat and rest, covered, for 5 minutes.

Heat a Dutch oven over medium heat. Add the sausage rounds and brown for 3 to 4 minutes, turning once. Transfer the sausage to a plate.

Add the oil and flour to the pot. Cook over medium-low heat, whisking constantly, for 12 to 15 minutes, until the roux is deep brown and smells toasted. If black flecks appear, start the roux again.

Stir in the onion, bell pepper, celery, remaining salt, black pepper, paprika, thyme, and cayenne. Cook for 6 to 8 minutes, until softened. Add the garlic and cook for 30 seconds.

Gradually whisk in the warm broth, then add the Worcestershire sauce and bay leaves. Scrape up any browned bits and bring the gumbo to a gentle simmer.

Return the sausage to the pot. Simmer uncovered for 12 to 15 minutes, until the vegetables are tender and the broth lightly coats a spoon.

Lower the heat and add the whole shrimp. Cook for 3 to 5 minutes, stirring gently, until the shrimp are opaque, pink, and loosely curled.

Remove the bay leaves. Spoon rice into bowls, ladle the gumbo over it, and scatter chopped parsley on top.