Spray 10 X 10 X 3 (or 9 X 13) casserole dish with nonstick spray. Preheat oven to 350 F.
Place sliced squash in microwaveable dish. Add 1/4 cup water and cover. Cook yellow squash in microwave for 5 minutes. Stir. If needed, cook another 2 minutes or until slightly tender. Drain. (Or you can cook the squash on stovetop if you wish. Combine squash with 1/2 cup water in a Dutch oven and bring liquid to a boil. Cook for 5-7 minutes, or until squash is just tender. Drain. Then you can use the empty Dutch oven for the next step.)
Meanwhile heat butter in Dutch oven over medium high heat and sauté onion, bell pepper, celery for about 7 minutes, stirring frequently.
Add garlic and cook 1 more minute.
Add chicken broth, Cajun seasoning, dried thyme, Tabasco and green onion tops. Lower heat to medium and cook 10 minutes.
Raise heat to medium high. Add the shrimp. Cook 5 more minutes, stirring from time to time. Remove from heat.
Add breadcrumbs, parsley, and basil. Mix well.
Add beaten egg and continue to mix.
Fold in drained squash.
Stir in all but 2 tablespoons of Parmesan cheese.
Pour mixture into prepared casserole dish, sprinkle with reserved Parmesan cheese, and bake uncovered at 350 for 30 minutes or until golden brown on top.
Allow to cool for 5 minutes and serve.