In a heavy bottomed sauce pan (like an iron skillet), melt the butter over medium-high heat. Next, whisk in the flour to form a roux. Continue whisking and cooking until the roux begins to change color.
When the roux has turned a light golden brown, add the trinity: celery, bell pepper, and onion and saute until the vegetables become tender.
Once the vegetables are tender, add the spice and garlic and saute for about 30 seconds.
Add the broth a little at a time, stirring to bring all the ingredients together to form a thickened gravy.
Stir in the crawfish tail meat, and then the cream and lemon juice.
Simmer on low heat for about 20 minutes.
Serve over hot cooked rice and garnish with parsley.