For the cheesecake:
Line a medium (about 23-cm wide) sieve, fine strainer or colander with a double layer of damp cheesecloth and set over a bowl.
Beat the cream cheese in a large bowl with a hand-held mixer on medium speed until smooth. Add the sugar, lime zest and juice and vanilla. Beat until light and fluffy, scraping the sides of the bowl and beaters as needed.
In another bowl, beat the cream until it holds a stiff peak. Stir about 1/3 of the whipped cream into the cream cheese mixture to lighten the cream cheese. Gradually fold in the remaining whipped cream to make a light mousse. Transfer the mixture into the lined sieve, fold the cheesecloth over the top and press gently. Cover and refrigerate to drain for at least 4 hours or up to 3 days.
Just before serving, cook about half the blueberries in a small skillet with the water and sugar, over a medium heat, until the berries get juicy, about 8 minutes. Toss all the berries together in a large bowl, along with a squeeze of fresh lime juice.
Unwrap the cheesecake and invert onto a platter. (Discard the cheesecloth.) Use a large ladle or spoon to press a well in the centre of the cake. Spoon the berries into the well and drizzle the juices over the top or serve on the side. Serve a scoop of summer cheesecake with some of the fresh berries.
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