Preheat your oven to 180°C (350°F). Pulse the flour, 125g butter, and caster sugar in a food processor until the mixture resembles fine breadcrumbs. Add the egg yolk and water, pulsing until the dough just comes together.
Roll the pastry out on a lightly floured surface and gently press it into the tart tin. Trim the edges, prick the base with a fork, and chill in the fridge for 20 minutes.
Line the pastry with parchment paper, fill with baking beans, and blind bake for 15 minutes. Remove the paper and beans, then bake for another 10 minutes until the shell is pale golden. Allow to cool completely.
To make the caramel, heat the 200g granulated sugar in a clean, heavy-bottomed saucepan over medium heat. Do not stir; swirl the pan occasionally until the sugar melts into a dark amber liquid.
Carefully stir in the 100g of softened butter using a whisk until fully incorporated. Be cautious as the mixture will bubble vigorously.
Slowly pour in the double cream while whisking constantly. Continue to cook for 2–3 minutes until smooth and thickened to a coating consistency. Remove from heat and stir in half of the sea salt.
Pour the warm caramel into the cooled pastry shell. Smooth the top with a spatula and sprinkle the remaining sea salt over the surface.
Chill the tart in the refrigerator for at least 3 hours, or until the filling is firm to the touch, before slicing and serving.