Make the Creole sauce: in a small bowl, whisk together 1/2 cup mayonnaise, 2 tablespoons Creole mustard, 1/2 teaspoon Creole seasoning, and 1/2 teaspoon paprika. Refrigerate until ready to serve.
Heat 1 tablespoon vegetable oil in a large cast iron skillet over medium-high heat. Add the diced russet potato and cook, stirring frequently, 8–10 minutes until potatoes are softened and starting to brown.
Add 1 tablespoon butter, the diced onion, diced bell pepper, and sliced Andouille sausage to the skillet. Cook 3–4 minutes, stirring, until the vegetables soften and the sausage browns.
Add the shrimp, 1 teaspoon Creole seasoning, 1/2 teaspoon paprika, and 1/4 teaspoon garlic powder. Cook 2–3 minutes until the shrimp are opaque and just cooked through.
In a bowl, whisk together the 7 eggs and 1/4 cup whole milk. Pour the egg mixture into the skillet and cook over medium heat, stirring gently with a rubber spatula, until the eggs are almost set.
Sprinkle 2/3 cup shredded Colby Jack or cheddar cheese evenly over the eggs, then place the skillet under a broiler briefly until the cheese melts and is lightly browned.
Remove from the oven, drizzle with Creole sauce if desired, and serve immediately.