Prepare the Roux: In a large skillet, melt the butter over medium heat. Add the flour, stirring continuously to form a roux. Cook until the mixture turns a golden brown color.
Sauté the Vegetables: Add the chopped onions, celery, green bell pepper, and minced garlic to the roux. Sauté until the vegetables are softened and aromatic.
Incorporate the Cream: Gradually whisk in the half-and-half, ensuring a smooth consistency. Continue stirring until the mixture thickens.
Add the Crawfish: Reduce the heat to low and add the crawfish tails. Cook for about 5 minutes, allowing the flavors to meld.
Melt the Cheeses: Stir in the shredded Monterey Jack and sharp cheddar cheeses until fully melted and the sauce is smooth.
Season the Fondue: Add the Cajun seasoning, salt, and black pepper to taste. Stir in the chopped green onions and parsley.
Serve: Transfer the fondue to a heat-resistant serving dish or fondue pot. Serve hot with cubes of French bread for dipping.