Step 1

Prepare the following, adding each to the bowl of a food processor fitted with the blade attachment as you complete it: Cut 1 small shallot into quarters. Cut 1/2 small green or red bell pepper into 8 pieces. Quarter 1 large garlic clove. Pick the leaves from 10 fresh parsley sprigs.

Step 2

Add 1 teaspoon of the Creole seasoning and pulse until coarsely chopped, about 4 (1-second) pulses. Scrape down the sides of the bowl with a spatula.

Step 3

Cut 1 pound peeled and deveined shrimp into 1-inch pieces, add to the food processor, and pulse until coarsely chopped, 4 to 5 (1-second) pulses, scraping down the sides of the bowl as needed. (Alternatively, finely chop all the ingredients by hand until no larger than 1/4-inch pieces remain.) Transfer to a large bowl.

Step 4

Juice 1/2 small lemon until you have 1 tablespoon plus 2 teaspoons. Add 1 tablespoon of the lemon juice to the bowl with the shrimp (reserve the remaining for the sauce). Add 1 large egg and 1/2 cup fine, dry breadcrumbs. Mix with a spatula until combined.

Step 5

Divide the mixture into 4 portions and shape each into a 3 1/2-inch wide patty (about 5 ounces each). Arrange in a single layer on a plate or parchment-lined baking sheet and refrigerate for at least 30 minutes and up to 24 hours.

Step 6

Meanwhile, let 2 tablespoons unsalted butter sit at room temperature to soften. Make the seasoned mayonnaise: Place 1/4 cup mayonnaise, the remaining 1/2 teaspoon Creole seasoning, and the reserved 2 teaspoons lemon juice in a small bowl and stir to combine. Refrigerate until ready to serve. Cut 4 slices crosswise from 1 medium tomato.

Step 7

When the patties are ready, split and butter the cut sides of 4 hamburger buns with the softened butter. Heat a 12-inch cast iron or nonstick skillet over medium heat. Place half of the buns cut-side down in the pan and cook until lightly toasted, 3 to 4 minutes. Transfer to a plate or cutting board and repeat toasting the remaining buns.

Step 8

Add 2 tablespoons vegetable oil to the pan. Reduce the heat to medium low. Add the patties and cook until golden brown on the bottoms, 4 to 5 minutes. Flip the patties and cook until cooked through, firm, and the centers register at least 120ºF on an instant-read thermometer, 3 to 4 minutes more. Remove the pan from the heat.

Step 9

Assemble the burgers: Spread each toasted bun half with a thin layer of the seasoned mayonnaise. Place a shrimp patty on each bottom bun. Top each patty with a slice of tomato, a butter or romaine lettuce leaf, and the top bun.