Heat the oil in a large heavy pot with a lid over high heat. Add the shallots, garlic, and cook, stirring, until soft. Season the red snapper, stripped bass, and shrimp with salt and pepper, add to the pot, and cook, stirring, until lightly browned on each side. Add the wine and cook until reduced by three-quarters. Add the stock, tomatoes, honey, a few dashes of hot sauce, bay leaf, and thyme, and bring to a simmer. Add the clams and lobster, cover the pot, and continue cooking until the clams have opened, discarding any that have not opened.

Remove the seafood with a skirted spoon and transfer to a large bowl. Bring the cooking liquid to a boil and cook until reduced by half. Whisk in the butter and parsely, and season with salt, pepper, and hot sauce to taster. Pour the broth over the seafood and serve.