Preheat the oven to 375℉ (190℃).
Line a baking dish with foil or parchment paper and spray with a nonstick cooking spray.
Place crabmeat in a large bowl and season with Creole seasoning. Or use just salt and pepper to season it.
Lightly beat the eggs, add the mayonnaise, and gently mix. Then, cover and refrigerate the mixture while preparing the other ingredients.
Melt butter in a skillet over medium heat. Add the onions, minced garlic, green onions, celery, red pepper, parsley, and more Creole seasoning. Sauté for 3-5 minutes and then transfer to a bowl. Let it cool.
While the sauteed ingredients cool, crush crackers until they have a fine crumb texture.
Once the sauteed veggies have cooled, gently fold the cream cheese, crushed crackers, sauteed veggies, parmesan, and seasoned crabmeat mixture until thoroughly mixed.
Test the mixture and adjust salt and pepper as needed.
Place shrimp on a cutting board and cut a slit in the underside about ¾ deep, stopping at the tail so they can lie tail up.
Season the shrimp lightly with Creole seasoning and salt if you desire.
Using a spoon, stuff each shrimp with 1-2 tablespoons of crabmeat. Carefully place the shrimp in your prepared baking dish, stuffed side up, and then spray them with cooking spray.
Bake the shrimp until golden brown (about 20 minutes).
Remove from the oven and serve right away.