Melt the butter in a large saucepan over medium heat.
Add the onions, bell peppers, and celery and cook, stirring, until the vegetables are soft and golden, 8 to 10 minutes.
Add the crawfish tails and cook, stirring occasionally, until they throw off some of their liquid, 6 to 8 minutes.
Dissolve the cornstarch in the water and add to the crawfish mixture. Simmer, stirring occasionally, until the mixture thickens, 4 to 5 minutes. Season with salt and cayenne.
Serve immediately over steamed rice.
Garnish with a sprinkling of green onions and parsley.