Puree the blackberries in a food processor or blender. Strain the puree through a fine sieve, pressing hard on the solids to extract as much puree as possible; discard the seeds.
In a large heavy saucepan, combine the half-and-half with the sugar and cook over moderate heat, stirring, until warm to the touch and the sugar has dissolved. Remove from the heat and stir in the dry milk.
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.
Freeze the custard in an ice cream maker, in 2 batches if necessary, according to the manufacturer's instructions. Transfer the gelato to an airtight container and press a layer of plastic wrap directly on the surface, then seal with a tight-fitting lid and freeze for at least 2 hours before serving.
The gelato can be frozen for up to 2 days. Let it soften for 15 minutes in the refrigerator before serving.