Mix any brown crabmeat with the crème fraîche and cayenne pepper, and set aside. Pull away any tough outer leaves from the fennel bulb (you can keep these to use for stock). Trim the base, and remove the stem (again, reserve these for making stock, if you like). Finely chop the fronds and set aside. Slice the bulb in half along the core, then lay the pieces, cut-side down, on a chopping board. Cut each half into thick slices, then rotate by 90 degrees and chop.
Heat the olive oil in a large, heavy-bottomed frying pan over a medium heat, add the fennel, shallot, chilli, garlic and a good pinch of sea salt and cook for 8-10 mins, or until the fennel and shallot are have softened. Add the tomatoes and cook for a few minutes more until they start to break down. Tip in the vermouth or white wine, and scrape up any browned bits from the bottom of the pan. Continue to cook until the liquid has reduced by about half, then remove from the heat.
Meanwhile, cook the linguine in a large pan of boiling salted water, following pack instructions, until just al dente. Reheat the fennel sauce over a medium heat and transfer the pasta directly from its water to the sauce using tongs. Add a good ladleful of the pasta cooking water to loosen the mix, then spoon in the white crabmeat. Stir everything together well to agitate the mixture and emulsify the sauce. Add the crab and crème fraîche mixture, and stir for a few minutes until the sauce is thick and glossy. Stir in the chopped herbs and taste for seasoning – the sauce should be thick, silky and not too runny, so continue to cook until it’s the right thickness, if needed. Season with a little lemon juice, then divide between warmed bowls.