In a medium bowl, lightly whisk the egg yolks. slowly whisk in 1/2 cup of the warm half-and-half mixture to temper the eggs, then gradually whisk in the rest. Return the mixture to the saucepan and cook over moderate heat, stirring constantly until it thickens to a runny custard and registers 180° on an instant-read thermometer, about 6 minutes. Remove the saucepan from the heat and stir in the heavy cream, blackberry puree and vanilla. Strain the custard through a fine sieve into a medium bowl set over ice water. Stir occasionally until the custard is completely chilled.