Boil: Bring a pot of water to a boil. Optionally, add salt and vinegar. Gently add cold eggs and lower heat to a simmer. Cook for 13 minutes, then transfer eggs to ice water for 15 minutes before peeling.
Sear: Pat shrimp dry and season with Cajun seasoning. Heat a skillet with 1 tablespoon of avocado oil over medium-high heat. Sear shrimp 1-2 minutes per side, then remove and set aside to cool.
Peel: Tap eggs gently to crack the shells, then peel them under cold running water. Slice eggs in half and remove yolks to a bowl. Mash yolks with a fork.
Mix: Add mayonnaise, Creole mustard, green onions, pickled jalapeños, hot sauce, and horseradish to the yolks. Mix until smooth and adjust seasoning. Refrigerate for 15-30 minutes.
Assemble: Transfer the filling to a plastic bag and snip the corner to pipe it into the egg whites. Garnish with Cajun seasoning or green onions if desired.
Serve: Top each deviled egg with a shrimp. Refrigerate before serving for the best flavor and texture.