In a medium size heavy bottomed Dutch oven, melt 2 tablespoons of the butter over medium-high heat and add the onion, bell pepper and celery. Cook, stirring occasionally, until the vegetables have softened and are lightly golden, about 6 minutes. Add the garlic, salt, cayenne and bay leaves and cook, stirring, for 2 minutes. Sprinkle the flour over the vegetables and cook, stirring and scraping the bottom of the pot, until the flour is lightly golden, 3 to 4 minutes. Add the crawfish stock and thyme sprigs and stir to combine. Partially cover the pot, reduce the heat to a simmer, and cook until any floury taste is gone and the sauce is flavorful, about 30 minutes. 

While the sauce is simmering, place the crawfish in a bowl and add the Essence, tossing them so that they are evenly coated. 

Stir the crawfish into the sauce and continue to cook over low heat until the crawfish are warmed through and their flavor has melded with the sauce, about 10 minutes. Stir in the remaining 4 tablespoons butter and the parsley and remove from the heat. Remove the thyme sprigs and bay leaves and discard. Serve in shallow bowls over hot white rice.