Arrange duck so cavity faces you. Draw tip of a sharp knife along side of the breastbone, making sure knife stays against bone, to separate meat from breastbone. Rotate duck 90 degrees.
Starting at pointy (cavity) end of breast, draw knife along rib cage, lifting meat as you separate it from ribs. Repeat on other side.
Score the duck breast skin (but not the meat) in a cross pattern. This helps the fat render and will give you a crispier skin. Place both skin-on breasts on a plate and set in refrigerator until ready to use.
Take the remaining duck carcass and season all over with 1 teaspoon salt.
Heat 2 tablespoons of vegetable oil in a large Dutch oven on a stovetop burner over medium-high heat. Add duck carcass (without the breasts) and fry for about 5 minutes until browned on all sides.
Add the chicken broth, Worcestershire, and Tony's seasoning to the Dutch oven. Bring it to a boil then reduce the heat to medium-low and simmer for about 2 hours until duck is tender.
Using tongs, carefully remove the duck pieces from the pot and let cool, then remove the meat from the bones, discarding the bones. Pour the broth and meat mixture into a large mixing bowl and set aside.
Using the same Dutch oven, warm ¼ cup vegetable oil over medium heat until hot. Add butter and whisk in flour, 1 tablespoon at a time and cook, whisking constantly for about 10 minutes until the roux becomes smooth and fragrant but doesn't take on much color.
Carefully add the onion, bell pepper, celery, minced garlic, 1 ¼ teaspoons salt and black pepper. Stir with a wooden spoon until the vegetables begin to soften, about 5 minutes.
Add sausage and reserved meat and broth mixture back into the Dutch oven, bring to a boil, then immediately reduce heat to medium low. Simmer, uncovered, for 20 minutes.
Meanwhile, take the duck breasts out of the refrigerator and pat them dry with paper towels. Season them with the remaining ¼ teaspoon salt.
In a large skillet with 1 tablespoon of vegetable oil lay the duck breasts skin side down then turn the heat to medium-high and cook for about 5 minutes. Then flip them over and cook for another 3 minutes until an instant read meat thermometer shows it at 130 degrees F. Transfer the duck to a cutting board and let it rest, skin side up.
To the etouffee mixture in the Dutch oven, stir in gumbo file and hot sauce.
At this point you want to taste it and add more seasonings to your liking. Maybe a dash more salt or Tony's.
Serve warm over rice with a few pieces of the crispy duck breast on top. Garnish with fresh parsley or chopped green onions.