Cut the kernels off the ears of corn and place in a large pot; break the cobs in half and add them to the pot. Add the cream, milk and 1 cup of the sugar. Stir well and bring to a boil over medium-high heat.
Off heat, remove the corn cobs (do not throw away). Use an immersion mixer or blender to puree the mixture, then return the cobs to the pot. Let the mixture stand for about 2 hours, keeping warm over the lowest setting of your stove.
After 2 hours, bring the mixture back to a simmer then remove from heat. Remove and discard the corn cobs. Whisk the egg yolks and remaining ½ cup sugar together in a bowl. Stir 1 cup of the hot cream into the yolk mixture to temper, then slowly pour the egg mixture into the cream mixture, whisking constantly.
Return the pot to the stove and cook over medium-low heat, stirring frequently, until mixture thickens and coats a spoon. This should take about 10 minutes.
Finally, pour the ice cream mixture though a fine sieve or strainer into a container to remove the pieces of corn. Chill the mixture for at least 4 hours or overnight before freezing in an ice cream maker according to manufacturer’s directions.
To make the blackberry sauce, bring the water and sugar to a boil in a large saucepan. Add the blackberries and cook for about 10 minutes or until the berries start to break down. Add the lemon juice and remove from heat. Use an immersion mixer or a blender to puree the blackberry sauce and then strain the sauce through a fine sieve or cheesecloth to get rid of the seeds. Refrigerate the sauce until you are ready to serve.
To serve, scoop the sweet corn ice cream into serving bowls and top with some of the blackberry sauce.