Heat oil in a skillet over medium heat and cook ground beef until browned, breaking it apart as it cooks. Browning adds deep flavor and forms the foundation of dirty rice. Drain excess grease if needed before moving on.
Add onion, bell pepper, and celery to the cooked beef. Let them cook until soft and aromatic, then stir in garlic briefly so it doesn’t burn. This step builds the signature Cajun flavor base.
Add Cajun seasoning, thyme, and black pepper, then pour in broth to loosen the mixture. Fold cooked rice into the pan and stir gently so the grains stay fluffy. Keep warm while preparing the sauce.
Melt butter in a saucepan and whisk in flour to create a light roux. Slowly add seafood stock and heavy cream while whisking to avoid lumps. Continue cooking until the sauce thickens smoothly.
Stir crawfish tails, Cajun seasoning, smoked paprika, and hot sauce into the sauce. Simmer briefly, then add lemon juice to brighten the flavor. Spoon the sauce generously over warm dirty rice when serving.