Preheat oven to 350 degrees F.
Melt butter in pot set on medium-high heat. Add onion, celery, and bell pepper. Saute until wilted, about 8 minutes.
Take off heat. Crumble cornbread into pot. Add salt, pepper, oysters, eggs, Cajun seasoning, chicken broth, and parsley. Mix thoroughly.
Pour into a buttered casserole dish and bake until golden brown, about 30 minutes.