Heat oil in a 12-inch skillet over medium-high. Add crawfish tail meat, and cook, stirring occasionally, until lightly browned, about 5 minutes. Transfer to a plate, and set aside.
Melt butter in skillet; add onion, bell pepper, celery, and jalapeño to skillet, and cook, stirring often, until translucent, about 6 minutes. Stir in mustard greens, and cook, stirring often, until tender, about 6 minutes. Add garlic, and cook, stirring constantly, 30 seconds.
Add tomatoes, water, vinegar, and salt to skillet; stir and bring to a boil. Reduce heat to medium-low, and simmer, stirring occasionally, 20 minutes. Stir in crawfish tail meat. Break eggs, 1 at a time, and slip into tomato sauce. Cover and simmer until eggs are cooked to desired doneness (3 minutes for runny yolks and 5 minutes for slightly runny yolks). Top with parsley and scallions. Serve immediately with, if desired, hot sauce.
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