While your shrimp stock simmers, you'll accomplish most of your mise en place. First, bring the shrimp shells and chicken broth to a boil in a medium saucepan, then reduce to a simmer for 20 minutes to extract flavor. While this develops, finely dice the onion, bell pepper, and celery (this is the holy trinity of jambalaya); mince the garlic; slice the turkey sausage into 1/2-inch rounds; peel and devein the shrimp; and thinly slice the scallions, keeping whites and greens separate. Strain the shrimp stock through a fine-mesh sieve, discarding the shells—you should have about 3 1/4 cups of flavorful liquid ready to go.
Heat the olive oil in a large pot or Dutch oven over medium-high heat. Add the sliced turkey sausage and brown it for 3-4 minutes, stirring occasionally—this renders fat and creates a flavorful base. Add the diced onion, bell pepper, and celery (your prepped trinity) and sauté for 5-6 minutes until softened and fragrant. Stir in the minced garlic and tomato paste, cooking for another 2 minutes to deepen the flavors and eliminate the raw garlic bite.
Stir in all the dried spices—bay leaf, thyme, oregano, smoked paprika, and cayenne pepper—along with the Tabasco sauce. Cook for about 30 seconds to bloom the spices and release their aromatics. Add the fire-roasted diced tomatoes (with their juices) and the brown rice, stirring well to combine everything evenly. I like to use fire-roasted tomatoes in jambalaya because they add a subtle smokiness that enhances the overall depth of the dish.
Pour in 3 cups of the prepared shrimp stock and stir to combine. Bring the mixture to a boil over medium-high heat, then reduce to low heat, cover with a lid, and simmer for 50-55 minutes until the rice is tender and most of the liquid is absorbed. The jambalaya will look slightly soupy at this stage—that's normal. Try not to stir during cooking, as this helps the rice cook evenly and prevents it from becoming mushy.
Remove the lid and stir in the peeled shrimp, fresh lemon juice, and the scallion whites (saving the greens for garnish). Cover and cook for 7-8 minutes until the shrimp are bright pink and cooked through—they'll be tender and should still have a slight bounce when pressed. If there's still visible liquid in the pot after the shrimp are cooked, uncover and cook for an additional 1-2 minutes to evaporate it. Season with additional salt and pepper to taste.
Divide the hot jambalaya into bowls or plates and top with the reserved scallion greens for a fresh pop of color and mild onion flavor. Serve with extra Tabasco or your preferred hot sauce on the side so guests can adjust the heat to their liking.