For the churros, heat the oil in a deep-fat fryer to 180C. Alternatively, heat the oil in a deep heavy-based frying pan until a breadcrumb sizzles and turns brown when dropped into it. (CAUTION: Hot oil can be dangerous. Do not leave unattended.)
Heat the butter with 125ml/4fl oz water in a saucepan until the mixture boils, then boil for another minute.
Remove from the heat and beat in the flour and cayenne with a wooden spoon until smooth, or until the mixture comes away from the side of the pan. Return the pan to the heat and cook for 1-2 minutes, stirring continuously.
Remove the pan from the heat and beat in the eggs, one at a time, beating well before adding the other egg.
Stir in the white and brown crabmeat until well combined, season with salt and pepper.
Spoon the mixture into a piping bag and pipe 1.5cm/½in long sections into the oil and fry for 1-2 minutes, or until golden-brown and crisp. Remove the churros and set aside to drain on kitchen paper, season with salt.
For the chilli jam, heat the sugar in a heavy-based saucepan over a medium heat until it melts and forms a golden-brown caramel (CAUTION: boiling sugar is extremely hot. Handle very carefully.)
Blend all of the remaining chilli jam ingredients, except the crème fraîche, in a food processor to a smooth purée.
Once the sugar has caramelised, add in the purée and stir well. Bring the mixture to the boil, then reduce the heat and simmer for 4-5 minutes, or until sticky and jam-like. Remove from the heat and set aside to cool. Once cool, stir in the crème fraîche until well combined.
For the dressed crab place the egg yolks, vinegar and mustard in a food processor and blend until pale and creamy. With the motor running, pour in enough oil, in a steady stream, to make a thick mayonnaise. Mix in the lime zest and juice. Mix 4 tablespoons of the mayonnaise into the fresh white crab.
For the salad, mix the leaves in a large bowl and dress with a little of the chilli jam.
Serve the salad leaves on a serving plate with the dressed crab, churros and chilli jam.