For the stone crab stock
Pick the meat from the crab, reserving the shells; you should have about 4 cups shells. Refrigerate meat until ready for use.
Heat oil over medium heat in large saucepan. Add crab shells and cook, stirring, until fragrant, about 2 minutes. Add onion, carrot, garlic, parsley, and bay leaf; cook until soft, 5–7 minutes. Add tomato paste and cook, stirring, until it darkens, about 1 minute. Add brandy and scrape up any bits from the bottom of the pan. Add water, bring to a boil, then reduce to a simmer; cover and cook for 30 minutes. Strain into a bowl through a finemesh strainer, pressing on solids to extract liquid. Discard solids.
For the sauce
Melt butter in a medium saucepan over medium heat. Add shallots and cook until softened, about 2 minutes. Stir in flour, tomato paste, and thyme; cook until flour turns light brown, about 1 minute. Add wine, bring to a simmer and cook until very thick and partially reduced, about 5 minutes. Whisk in stock and cream and bring to a simmer. Cook, whisking occasionally, until reduced by half, 25-30 minutes. Reduce heat to low, stir in brandy and saffron and let steep for 20 minutes. Season with salt and pepper.
Heat oven to 400°. Season fish with salt and pepper and lightly dust with flour. Heat oil in medium skillet over medium heat; add fish and cook until golden on one side, about 2 minutes. Turn fish and add ½ cup of the sauce to pan. Transfer pan to oven and bake until white fat bubbles from fish and is cooked through, about 7 minutes. Transfer fish to serving plate. Lightly baste reserved crab meat with sauce to warm through, being gentle not to break up chunks. Perch crab on top of fish and drizzle with sauce. The sauce is rich, as is the crab, so use restraint so the fish and crab are the stars of the show.
Blue Marlin: 121 Bridge St, Bradenton Beach; 941-896-9737; bluemarlinami.com