Up to two days ahead:
Heat 1 Tbs. each of the oil and butter over medium-high heat in a large (at least 6-quart) Dutch oven. Season the chicken liberally with salt and pepper. Add half of the chicken pieces and sear until golden brown on two sides, about 6 min. For best browning, stir infrequently and only to flip the chicken. Repeat with the remaining chicken, reducing the heat if the bottom of the pan starts to burn. Set all the chicken aside.
Lower the heat under the Dutch oven to medium and add another 1 Tbs. each of oil and butter. When hot, add the celery, peppers, and onion. Sauté until the vegetables are softened and lightly browned, 6 to 8 min. Add the garlic and cook, stirring, for another 2 minutes. Push the vegetables to one side of the pan and add the remaining 1 Tbs. oil. Add the curry spice blend, thyme, 1 tsp. salt, and 1/2 tsp. black pepper to the oil. Cook, stirring, for 1 min. Raise the heat, add the tomatoes and their juices, and bring to a boil. Cook, stirring, until the tomatoes begin to break apart and the juices thicken slightly, about 5 min. Stir in the chicken broth and currants; return the mixture to a boil. Adjust the heat to maintain a vigorous simmer and cook, stirring occasionally, until slightly thickened, about 15 min.
Return the chicken and any accumulated juices to the pot; simmer for about 10 min. Season to taste with salt and pepper. (If you’re working ahead, the stew may now be cooled and refrigerated.)
Just before serving:
Bring the stew to a simmer over very low heat. Add the shrimp and simmer, stirring, until they just turn opaque and are cooked through, 3 to 4 min. Divide the rice among eight shallow soup bowls and spoon the stew on top. Sprinkle each serving with the chopped parsley and serve.