How to Make It
Pour the mochiko flour into a baking tray and roast for 35 minutes at 350°, turning halfway through. As the flour roasts, combine the shrimp shells, clam juice and chicken broth in a stockpot; simmer for 20 minutes over medium heat, then strain and set aside, discarding the shells.
Rinse the stockpot, then return to the stove. Add the butter and warm over medium heat. Add the mochiko and stir to combine. Toast until a rich brown color, about 20 minutes total, stirring constantly to prevent scorching.
Add the celery, onion and bell pepper and sauté, stirring often, until softened, about 5 minutes. Stir in the garlic and sauté until aromatic, about 1 minute. Add the crushed tomatoes and broth, then stir to combine. Bring to a simmer and reduce heat to medium-low. Simmer until the flavors combine, about 1 hour, stirring often.
Stir in the carrot, okra, chile powder, paprika, salt, thyme, pepper and optional cayenne or hot sauce. Simmer until the carrot is slightly tender, about 10 minutes, then taste and add salt if needed.
In a small skillet, warm the olive oil over medium heat, then add the sausage slices. Brown the sausage on each side, about 3 minutes per side, then add to the gumbo. Add the shrimp to the gumbo and simmer until pink and curling, about 2 minutes. Serve as-is or over white rice.