In a heavy bottomed saucepan, heat the water and sugar over medium heat. Stir constantly until the sugar has dissolved, then increase the heat to high and bring to a boil, without stirring. Let the mixture continue boiling until it turns an amber color. This will take about 5-10 minutes.
Remove from the heat and slowly whisk in the heavy cream, taking care since the mixture will bubble up. Mix in the butter, vanilla, and salt. Pour the caramel sauce into a heatproof dish and allow to cool completely.
Combine cream and milk in medium bowl. Add egg, egg yolks and cornstarch to a separate medium bowl and whisk until smooth. Set aside
Stir brown sugar, water and salt in a medium sized pot over medium-low heat until sugar dissolves. Increase heat to medium-high and bring to a boil. Swirl the pot occasionally but do not stir, and brush down the sides of the pot with a wet pastry brush. Boil until mixture turns dark amber in color and has a thick, syrupy texture, about 5-7 minutes.
Immediately whisk in cream mixture (take care as mixture will bubble up) and whisk constantly to dissolve the caramel bits. Bring the mixture to a boil (keep an eye on it to prevent the pot from boiling over), then reduce heat to a gentle simmer.
Pass mixture through a fine mesh strainer into a container. Cover and refrigerate until chilled, about 4 hours.
Pour about 2 tablespoons each of caramel sauce into 4 small glasses or jars. Heating it for about 30 seconds in the microwave will make it easier to pour. Allow caramel sauce to cool a bit before adding the budino.
Divide budino evenly amongst jars.
To make the whipped cream, combine 1/2 cup of heavy cream with the confectioners sugar in an electric mixer and whip until smooth peaks form.
Top each budino with dollops of fresh whipped cream, a sprinkle of sea salt and shortbread crumbles.