Fill a large Dutch oven with several inches of water. Bring to a boil. Boil half of the bell pepper halves for 7 minutes. Remove from the water and allow to drain and cool. Repeat with remaining bell pepper halves. Allow to cool. Dump water from Dutch oven and return to stove to use with remaining steps of the recipe.
Meanwhile, place shrimp in colander and sprinkle with 1 teaspoon of Cajun seasoning. Stir to distribute seasoning, then allow shrimp to sit while you cook the trinity.
Preheat oven to 375 degrees. Decide what size baking pan will work best for the number of peppers you want to bake. (You may want to freeze some prepared peppers for later baking.)
Melt 1 tablespoon of butter and 1 tablespoon of vegetable oil in Dutch oven over medium high heat. Add chopped onion and cook, stirring now and then for 5 minutes. Add chopped bell pepper, celery, and white parts of green onions. Sauté for another 5 minutes until vegetables are wilted. Add garlic and chopped thyme and continue cooking for 1 minute.
Add shrimp pieces to vegetable mixture and cook until the shrimp pieces are just turning pink. Remove the pan from heat.
Add crumbled cornbread to the shrimp mixture and stir. Add 1 cup of broth, eggs, sage, Tabasco, sliced green onions, chopped parsley, and remaining 1 teaspoon of Cajun seasoning to cornbread and shrimp mixture. Fold to mix well. If more moisture is needed, add remaining broth in increments of about 2 tablespoons until desired consistency is reached.
Using a spoon, scoop cornbread-shrimp mixture into bell pepper halves, making sure to get stuffing into curves and crevices of the hollowed-out peppers. Mound stuffing on top for a rounded appearance. If you are going to freeze any peppers, move them to a plate to prepare for freezing later.
Place peppers to be baked stuffing-side-up in an appropriate size baking pan. Dot the top of each pepper’s stuffing with 1 teaspoon of butter divided into small pats.
Bake the peppers uncovered at 375 for 25 minutes. Remove from oven. Garnish with additional parsley and fresh thyme, if desired.