In a small saucepan over medium-low heat, warm stock with pot covered. Once stock starts to steam, remove from heat and let sit, covered, until ready to use.
Meanwhile, in a large cast-iron skillet or Dutch oven over low heat, melt butter. Add flour and cook, whisking constantly, until roux is a medium-brown caramel color, 5 to 6 minutes. Do not let roux burn.
Add onion, bell peppers, and celery and cook, stirring occasionally, until softened, about 7 minutes. Add garlic, Cajun seasoning, salt, and cayenne cook, stirring, until fragrant, about 1 minute more. Add warmed stock and bring to a simmer. Partially cover skillet, reduce heat to low, and simmer, stirring occasionally, until liquid is slightly reduced and flavors have melded, 15 to 20 minutes.
Stir in crawfish and cook, tossing, until warmed through, about 2 minutes.
Divide rice among bowls or plates. Spoon étouffée over, then top with parsley.
