Preheat the grill to medium-high and set a large, heavy cast iron skillet directly on grate. Place the chicken thighs and sausage on the grill alongside it and cook, turning, until charred and cooked through. Remove to a wood cutting board and when it's cool enough to handle, cut into bite-sized pieces.
Meanwhile, add a drizzle of oil to the skillet, and when it's hot add the onion, bell pepper, celery, and garlic. Cook, stirring often, for 4-5 minutes or until softened. Add the tomato paste and cook for another minute, then stir in the tomatoes, scraping up browned bits. Mix in the rice, spices, thyme and bay leaves. Add the stock; season with salt and pepper and bring to a simmer. Move the pan to a cooler spot (or reduce the heat), cover with foil, and simmer until almost all the liquid is absorbed, 20–30 minutes.
Season shrimp with salt and pepper; quickly cook on the hot grill, then mix into the rice along with the chicken and sausage. Toss to combine and top with parsley.