Heat the butter in a large saute pan or skillet over medium. Stir in the flour to form the roux. Stir with a flexible rubber spatula for 8 to 10 minutes, until the roux begins taking on a light caramel color. Keep the roux moving around the pan, so it doesn't burn. Adjust the heat down, if necessary, to prevent scorching.
When the caramel color is reached, add the onions, peppers, celery, and 1 teaspoon kosher salt. Add a pour or two of the broth to loosen the vegetable mixture.
Sprinkle the Creole seasoning over the vegetables and mix well. Stir in the tomatoes with their juices.
Add another cup of broth. The mixture should be thick and slightly soupy. Add more broth, if necessary.
Let the etouffee come to an active simmer, then add the shrimp. Cook for about 10 minutes, or until the shrimp are opaque and pink. Garnish with green onions and parsley.