1. In a small nonstick skillet heat butter over medium heat. Add bell pepper, onion, and ¼ teaspoon on the salt. Cook, stirring occasionally, until vegetables are soft and just begin to brown, about 6 minutes. Set aside to cool.
2. Meanwhile, place half of the shrimp and remaining salt in a food processor. Blend on high, scraping down the sides until a smooth, white, fluffy paste has formed. 
3. Chop remaining shrimp into ¼-inch pieces. 
4. Transfer shrimp paste and chopped shrimp to a large mixing bowl. Add sauteed vegetables, breadcrumbs, 1 tablespoon of the creole seasoning, and 1 tablespoon of the mayonnaise. Stir to combine. Form into four patties, each about 1-inch thick.
5. In a nonstick skillet heat oil over medium heat. Add shrimp burger patties. Cover pan, cook 6 minutes, adjusting heat as needed to prevent burning. Flip burgers, continue cooking uncovered until golden brown on the outside and burgers register 160°F on an instant-read thermometer inserted into the middle of one of the burgers, about 6 to 8 minutes more.
6. While the burgers are cooking, stir together the mayonnaise and remaining tablespoon of creole seasoning. Set aside until ready to serve.
7. To build a burger, add lettuce to the bottom of one of the buns. Place shrimp burger on top of lettuce. Add 2 tablespoons of the creole mayonnaise on top of the shrimp burger and add top bun. Repeat with remaining ingredients.

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