Special equipment: a piece of cheesecloth and some kitchen twine
Heat 1/2 cup of the vegetable oil in a cast-iron or other heavy-bottomed skillet over medium-high heat until very hot. Add the flour and whisk until combined and just beginning to brown. Reduce the heat to medium-low and continue to cook, whisking occasionally, until it is a deep peanut butter brown color, 15 minutes. Set the roux aside.
Meanwhile, heat the remaining 1 tablespoon oil in a Dutch oven or large pot over medium heat. Add the sausage and cook, stirring occasionally, until the fat has rendered and is lightly browned. Remove the sausage with a slotted spoon to a bowl. Sprinkle the chicken pieces with 1 teaspoon salt and 1/4 teaspoon pepper and brown over medium heat in the sausage drippings. Remove the chicken from the pot and place in the bowl with the sausage. Stir in the tomato paste until smooth and slightly darkened (be careful not to burn), about 1 minute. Add the celery, onions, peppers and cayenne to the pot and continue to cook until softened, 8 to 10 minutes. Add the garlic and cook until just aromatic, about 30 seconds. Add the chicken broth and 2 cups water and bring to a simmer. Slowly whisk in the warm roux a bit at a time until combined. Tie the pickling spice in a bit of cheesecloth and add to the pot along with the chicken and sausage. Simmer all together until thickened and the flavors have blended, about 45 minutes.
Add the shrimp and gumbo file and simmer until the shrimp are just cooked through and the gumbo has thickened, about 5 minutes. Remove and discard the pickling spice bundle. Taste and adjust the seasoning with additional salt and pepper. Serve the gumbo over rice.
Pickling spice contains chiles, coriander, cumin, ginger, black pepper, allspice, cinnamon, bay leaves, brown mustard, yellow mustard, cloves and turmeric. You can make your own if you can't find it at the market.