Heat 1 teaspoon oil in a 6+ quart Dutch oven or soup pot over medium-high heat. Add sausage and sauté until browned, 5 to 7 minutes. Transfer to a plate then set aside. Season both sides of chicken thighs with 1 teaspoon Cajun seasoning and place skin side down in Dutch oven. Sear on both sides until golden brown, 3 to 4 minutes a side (does not need to be cooked through), then transfer to plate with sausage and set aside.
Remove Dutch oven from heat for a few minutes to cool slightly and place back over medium heat. Add remaining 3 tablespoons oil then sprinkle in flour and whisk constantly until mixture is the color of caramel, 10 to 15 minutes (this is your roux). Add bell pepper, celery and shallot or onion and sauté until vegetables are slightly tender, 5 minutes, scraping the bottom of the Dutch oven often with a wooden spoon to make sure roux doesn’t burn. Add garlic and tomato paste and sauté for one more minute.
Add a couple big glugs of chicken broth at a time to the Dutch oven, using the wooden spoon to scrape up any bits on the bottom. Add remaining chicken broth, remaining 1 tablespoon Cajun seasoning, bay leaves, smoked paprika, cayenne pepper, sautéed sausage and chicken thighs and turn heat up to bring gumbo to a boil. Turn heat down to medium and simmer uncovered for 1½ hours, occasionally skimming off the fat that rises to the top.
Transfer chicken to a cutting board, removing and discarding skin and bones. Shred chicken and add back into the gumbo. Remove bay leaves then taste and adjust seasonings if necessary. Serve over cooked white rice.