In a bowl, scrape the butter into small pieces, then, whilst slowly adding the flour, press and mix the ingredients to make a crumble mixture. Once crumbly, add the icing sugar and happy egg yolks and mix through to bind the mixture loosely. (Remember when using the egg yolks to set aside the whites for later!)
If the mixture will not bind together, add 1 tsp of cold water and continue to mix. Only add 1 tsp of water at a time and never more than 4 tsp of water in total.
Place the pastry on a piece of cling film, wrap tightly, then roll into a sausage shape and place in the fridge for 60 minutes.
We need to blind-bake the tart base. On a floured surface, roll-out the pastry to a thickness of a £1 coin. Gently place the pastry in a floured biscuit baking tin and mould it into the corners with your fingers.
Prick with a fork all over, to stop it from rising and place in a preheated oven at 180°C for 8 minutes.
Remove from the oven, check for any holes or cracks and patch them with spare pastry. Allow the tart to cool for 5 minutes, glaze with the beaten egg white and place back in the oven for a further 2 minutes. Remove from the oven, and trim the edges with a sharp knife.
Place the cream, lime juice and zest into a saucepan, gently warming until bubbles start to appear around the sides, then it take off the heat and leave the flavours to infuse.
Soak the gelatine leaves in cold water for a few minutes until they are soft, then add to the warm cream mixture and lightly whisk. After 20 minutes, sieve the cream to remove the lime zest and any unmixed gelatine.
Make the custard by whisking the mixture together with the happy eggs, happy egg yolks, caster sugar, milk and salt. Whisk until smooth and fully combined.
Turn the oven down to 120°C/250°F/Gas Mark ½. Pour the custard into the tart base. Place in the oven and bake for 45 minutes. Check it’s cooked by lightly shaking the tin, the mixture should be firm but still a bit wobbly, like a jelly.
Leave to cool and serve in slices.