First make the lobster butter: twist off the claws from the lobster and use for another recipe. Cut the whole body including the tail and head in half lengthways. Remove the meat from the tail and body, cut into smallish pieces and put aside in a bowl. Cut the body, tail and legs into 2 inch/5 cm pieces.
Top and tail the chilli if used, cut into half lengthways, remove and discard the seeds. Melt the butter in a saucepan, add the lobster shell pieces the paprika, and the chilli and simmer over a low light for about ten minutes. Take off the heat, strain the butter through a sieve pressing down on the lobster pieces into a small bowl. Discard the lobster bits and allow the butter to cool right down to room temperature and then pop into the fridge or preferably freezer for a bit.
Peel and chop the shallot(s), roughly grind the peppercorns in a pestle and mortar, and add along with a glass of white wine, salt and the tarragon to a saucepan. Reduce over a medium heat to two or three tablespoonfuls of liquid.
Take out two tablespoonfuls of liquid and put into a saucepan along with three egg yolks, a tablespoonful the lobster butter and a squeeze of lemon juice. Put the saucepan on to a bain maree stand in another saucepan of boiling water.
Cut the remainder of the lobster butter into cubes and add slowly stirring with a wooden spoon. Towards the end increase the heat if necessary so that the sauce thickens. Season with further salt and lemon juice and thin with some warm water if required. Stir in the lobster pieces and serve.