For the sauce: Steam lobster for 15 minutes. Cool completely, 45 minutes to 1 hour, and remove the meat from the shells. Keep claw meat whole. Coarsely chop tail meat. Break up all shells and save for the sauce. Reserve lobster meat in the refrigerator.
Heat canola oil in saute pan and saute vegetables with thyme leaves until shallots are transparent. Add reserved lobster shells to pan and cook for 1 minute, stirring shells to completely heat and coat. Pour in sherry and then brandy to deglaze pan; simmer for 2 minutes. Add the chicken broth and simmer on low heat until reduced by half, about 4 minutes.
Mix in the tomato paste and add salt and pepper, to taste. Add the heavy cream, stir, and bring to a simmer. Simmer gently until cream and tomato paste bind, about 2 minutes.
Strain sauce in a strainer over a small bowl. Keep warm until other seafood is prepared.
For the seafood: Heat pan with canola oil to medium. In a small bowl mix together salt, pepper, thyme, and parsley. Liberally coat cod fillets with seasoning mixture, then drizzle with olive oil. Place fillets, skin side down, in hot saute pan. Allow fish to cook 3 to 4 minutes until skin side is crusted nicely, then carefully turn and cook 3 to 4 minutes on other side.
While fish is finishing, place a generous handful of field greens on each plate. Lean sauteed fish against the greens.
Quickly pour excess oil off from pan and saute shrimp until pink, about 1 1/2 minutes on each side. Lift out shrimp to plate and add chopped lobster and crabmeat to the pan. Add brandy cream sauce and heat mixture briefly until warmed. Pour half of seafood-cream sauce mixture over bottom half of each fillet. Garnish each plate with one lobster claw and two shrimp.
Recipe courtesy of Joe Gagliard, Fenway Park