Grease an 18cm springform cake tin and line the base with baking paper. In a small pan, melt 60g of the butter, then mix in the crushed shortbread with a wooden spoon. Press the mixture into the base of the tin with the back of the spoon. Put in the fridge to chill while you make the filling.
Put the gelatine in a shallow bowl and cover with cold water. Leave to soak for 5 minutes. Put the sugar and 50ml water in a heavy-based pan and gently heat, stirring until the sugar has dissolved. Bring to the boil and let it bubble for 2-3 minutes, without stirring, until the syrup is a deep golden caramel. Remove from the heat and add the remaining butter. Stir until the butter has melted, then stir in the cream and half the salt.
Return to a gentle heat and stir for 1 minute until smooth. Squeeze out the excess water from the gelatine and stir 1 sheet at a time into the caramel sauce. Transfer the sauce to a heatproof bowl and leave for 10-15 minutes, stirring occasionally.
Put the soft cheese in a large mixing bowl and gradually beat in the warm caramel sauce, until completely combined.
Spoon the mixture over the biscuit base, level the surface with the back of a spoon and chill in the fridge for 2-3 hours (or overnight, if making the day before), until set.
Put the chocolate in a small microwave-safe bowl. Microwave on low for 2-3 minutes, stirring halfway through, until melted.
Add the remaining salt and mix well. Use a teaspoon to drizzle it over the top of the chilled cheesecake. Return the cheesecake to the fridge for at least 5 minutes to set. Remove from the fridge 20-30 minutes before serving.