1) Fill a large heavy saucepan with 25-8cm of cooking oil and heat over medium-high heat. The oil temperature should be at 180C when you start frying.
2) In a large bowl, mix the eggs and milk; then add the flour and baking powder and mix thoroughly with a hand-held mixer. Strain the mixture to remove any lumps. Add more milk if you want a thinner crust. In a small bowl, mix the Cajun spice mix, cayenne pepper, white pepper, black pepper, dry mustard, and salt. Add this spice mixture to the batter. Cut the onions into thick slabs, dunk them in the batter, and fry them, in batches, in the oil until golden brown. Serve the onion rings with the Blue Cheese Dip, sliced carrot, and celery.
For the blue cheese dip:
In a large bowl, mix all the ingredients together. Season with salt and pepper, to taste. Serve the sauce in a side bowl for dipping.