How to Make It
In a large pot of boiling water, cook the lobster for 2 minutes. Drain and let cool slightly. Remove the meat from the tail and claws; cut the tail meat into 4 pieces. Reserve the lobster shells.
Heat a large saucepan. Add the lobster shells and the reserved shrimp shells and cook over high heat, stirring occasionally for 5 minutes. Stir in the tomato paste and cook for 2 more minutes. Add the brandy, ignite and cook until the flames subside. Add the ham hock and 8 cups water and bring to a boil. Lower the heat to moderate and cook until reduced by half, about 45 minutes. Remove the ham hock and cut 1/2 cup of lean meat off the bone; reserve the remainder for another use. Strain the broth and skim any fat; keep the broth warm.
Preheat the oven to 350°. Coat a smooth-bottomed nonstick oven-proof skillet with vegetable cooking spray and heat. Season the chicken with salt and pepper and cook over high heat, turning once, until golden, about 2 minutes per side; transfer to a plate. Coat the skillet with cooking spray, add the onion and garlic and cook until just translucent, about 4 minutes. Add the tomatoes, rice, paprika and saffron and cook until the liquid is absorbed, about 4 minutes.
Stir in the broth, ham hock meat, chicken, 1 teaspoon salt and 1/2 teaspoon pepper. Cover and bring to a boil over high heat. Reduce the heat to low and simmer, shaking the skillet for 10 minutes. Add the clams, mussels and lobster meat; cover and bake until the clams begin to open, about 10 minutes. Add the shrimp, peas and sugarsnaps and bake covered until the shrimp are cooked through, about 5 minutes. Let rest for 10 minutes, then serve.