Place the Dublin Bay prawns in a large pan and just cover with cold water. Bring to the boil, then remove from the heat and drain into a colander. The prawns should be cooked through but still very succulent and moist. Leave to cool.
Heat a large heavy-based pan with the olive oil. Add the raw prawns, onion and carrots and sauté for 3-4 minutes. Pour in the brandy and allow to bubble down, then stir in the tomato puree.
Pour in 1 litre/1 3/4 pints of water and bring to the boil, then reduce the heat and simmer for about 30 minutes until well flavoured and slightly reduced.
Remove the pan from the heat and strain the liquid through a fine sieve into a clean pan, then simmer until reduced by half.
Pour in the cream and simmer for another 5 minutes until reduced by half again. Season to taste and keep warm or leave to cool and reheat as required – you should have 400 ml/14 fl oz in total.
Place the prawn infusion in a small pan and add the Guinness, then allow to just warm through. Finally whisk in the butter. Arrange the cooked Dublin Bay prawns in old-fashioned pint glasses and place on serving plates. Pour the prawn and Guinness chaser into the espresso cups and set to one side.