For the tenderloin and pastry:
Line a large baking sheet with aluminum foil and grease the center with 1/2 tablespoon of the butter. Set aside.
Season the pork tenderloins on all sides with 1/2 teaspoon of the salt and 1/2 teaspoon of the pepper. Heat the vegetable oil in a large skillet over medium-high heat. Add the tenderloins; reduce the heat to medium, and brown evenly on all sides. Cook, turning frequently, until the meat reaches an internal temperature of 110 degrees F, 10 to 12 minutes. Remove the tenderloins from the skillet and allow to cool for 30 minutes.
In a clean, large skillet, heat the remaining butter over medium heat. Add the onions, celery, green bell peppers, and green onions. Saute until vegetables are tender and any released juices have evaporated, 6 to 8 minutes, stirring frequently. Add the thyme, Essence, 1/4 teaspoon pepper, a pinch of salt, and a pinch of cayenne, and cook for 1 additional minute. Remove the vegetables from the skillet and place in a bowl. Stir in the parsley and allow mixture to cool for about 10 minutes.
Set aside 1/2 cup of the vegetable mixture for the sauce. Divide the remaining vegetable mixture into 2 equal portions.
On a lightly floured work surface, lightly roll 1 sheet of the puff pastry to a 12 by 13-inch rectangle. Sprinkle 2 tablespoons of the bread crumbs evenly over the puff pastry, leaving a 1-inch border around the edges. Spread 1/4 cup of the grated cheese over the breadcrumbs.
Pat the seared tenderloins dry. Spread 1 half of the vegetable mixture onto half of the puff pastry, over the breadcrumbs and cheese. Place 1 tenderloin over the vegetables, so that it is parallel to the shorter side of the pastry. Whisk together the egg and 1 tablespoon of water. Brush the egg wash around the 1-inch border of the pastry. Gently lift the pastry around the tenderloin, and continue rolling the tenderloin in the pastry, jellyroll style. Use the egg wash to seal the edges of the pastry. Cut away any excess pastry and seal the edges closed by pinching them together, and folding them under the tenderloin.
Place the tenderloin, seam-side down, on the prepared baking sheet and repeat the process with the remaining vegetables, pastry, bread crumbs, cheese, and tenderloin. Make a decorative cross-hatch pattern across the tops of the pastries, being careful not to cut through the pastry. Brush the tops and sides of the pastries evenly with the remaining egg wash. Refrigerate the tenderloins in pastry for 30 minutes.
Preheat the oven to 400 degrees F.
For the Creole mustard cream sauce: Heat the reserved 1/2 cup of vegetables in a medium saucepan over medium-high heat. Add the flour and cook, stirring, for 2 minutes. Stir in the mustard and continue to cook for 1 more minute. Slowly whisk in the chicken broth and heavy cream. Bring mixture to a simmer and cook, over medium-low heat until sauce is reduced to about 1 1/2 cups, about 20 minutes. Season sauce with 1/4 teaspoon of salt and 1/4 teaspoon of freshly ground black pepper. Set sauce aside and serve warm or at room temperature.
Place the tenderloins in the preheated oven and bake for 20 to 22 minutes, or until golden brown and an instant-read thermometer inserted in the center registers 150 degrees F. Remove from the oven and let rest for 10 minutes before serving. Serve sliced, with the Creole Mustard Cream Sauce.
Emeril's ESSENCE Creole Seasoning (also referred to as Bayou Blast):
2 1/2 tablespoons paprika
2 tablespoons salt
2 tablespoons garlic powder
1 tablespoon black pepper
1 tablespoon onion powder
1 tablespoon cayenne pepper
1 tablespoon dried oregano
1 tablespoon dried thyme