Cut a neat circular lid around the pumpkin stem and lift it away. Scoop out all seeds and stringy fibers. Brush the cavity with 1 tablespoon olive oil, then season with half of the salt and the black pepper.
Set the pumpkin and lid on a sturdy baking dish. Roast until the flesh is tender but the shell still holds its shape. Set aside.
Melt the butter with the remaining tablespoon olive oil in a large skillet over medium-high heat. Add the shrimp and lobster in a single layer. Sear just until the shrimp turn pink and the lobster becomes pearly and opaque. Transfer to a plate, reserving several shrimp for the topping.
Reduce the heat to medium. Add the garlic and shallot to the foaming butter and cook briefly until fragrant. Stir in 1 tablespoon parsley and the smoked paprika, scraping up the browned bits.
Add the diced tomatoes and cook until they begin to soften. Pour in the coconut milk and heavy cream and bring to a gentle simmer. Add half of the Catupiry and stir until the sauce is thick, smooth, and glossy. Finish with the lime juice and remaining salt.
Return the seared shrimp and lobster to the skillet. Fold gently through the sauce only until evenly coated and warmed.
Spread the remaining Catupiry over the warm inner walls of the roasted pumpkin. Spoon the creamy shrimp and lobster filling into the cavity.
Top with mozzarella, the reserved shrimp, remaining parsley, and chives. Broil only until the cheese is melted, bubbling, and deeply golden in spots.
