In a 5- to 6-quart pot, toast the shrimp shells and the garlic clove over medium-high heat, stirring, until the shells turn pink, 1 to 2 minutes. Add the parsley sprigs and 2 cups water, bring to a boil, then boil for 3 minutes. Strain the broth into a bowl and reserve.
Heat the butter and olive oil in the cleaned pot over medium heat until the butter is melted. Add the chopped garlic and the shallot and cook, stirring, until the garlic is fragrant, about 1 minute. Add the wine and the reserved shrimp broth and bring to a boil over high heat.
Add the clams and mussels and cook, covered, until the mussels start to open, about 4 minutes. As they open, transfer them with a slotted spoon to a large, wide serving bowl or 4 large individual bowls. Continue to cook the clams, stirring occasionally, until they start to open, about 2 minutes more. Transfer them to the serving bowl. (Discard any clams or mussels that don’t open after 8 minutes.) Sprinkle with half of the chopped parsley.
Reduce the heat to medium and season the broth with salt and pepper to taste. Add the tomato, scallops, and shrimp to the broth, cover, and cook until the shrimp turn pink and the scallops are opaque, about 2 minutes. Transfer the shrimp, scallops, and broth to the bowl and sprinkle with the remaining chopped parsley.