Preheat your oven to 350°.
Heat 1 teaspoon oil in a deep skillet or dutch oven over medium-high heat. Once hot add in chicken and season with a pinch of kosher salt. Stir and cook until browned and fully cooked. Remove and transfer to a plate.
To the skillet, add an additional teaspoon olive oil to pan if needed, add the sausage and toss in oil. Spread in an even layer and cook until browned. Stir and repeat. Once browned, transfer to plate.
Reduce the heat to low and add the diced peppers, celery, onion, jalapeño and garlic with a pinch of kosher salt. Toss the veggies in the rendered sausage fat and sautè until tender.
Stir in tomato paste, cajun seasoning and smoked paprika and cook 1 minute.
Add in the crushed and diced tomatoes and broth, drop in the bay leaves. Increase the heat to high and bring to a boil. Stir in the rice, cover and slide the pan onto the middle rack of your preheated oven for 30 minutes. Stir the rice after the first 15 minutes.
Once the rice has cooked, stir in the raw shrimp, cooked chicken and andouille sausage. Cover and bake for an addtional 10 minutes or until the shrimp is opaque and fully cooked.
Season the jambalya with kosher salt to taste (about 1-1/2 to 2 teaspoons) before serving.
Serve with minced parsley, sliced green onons, a few dashes of hot sauce and homemade cornbread.