In a bowl, stir together 2/3 cup milk and the cornstarch; set slurry aside.

In a 4-qt. saucepan , combine the remaining milk and the cream, sugar, honey, buttermilk powder and salt. Add corn kernels. Using an immersion blender, blend together all of the ingredients until the corn kernels are all broken apart and the rest of the ingredients are well mixed.

Bring to a boil over medium-high heat and cook for 4 minutes. Stir often to ensure nothing is sticking to the bottom of the pan. Reduce the heat to medium-low.

Put the egg yolks in a medium-sized bowl and whisk them or mix them with an immersion blender. Take a small amount of the warm mixture and add it to the bowl with the egg yolks. Whisk the yolks and the mixture until well-blended, then add it all back into the saucepan. Add the slurry of milk and cornstarch.

Raise heat again to medium-high and return to a boil and cook, stirring, until thickened. Remove it from the heat. Pour mixture into a high-powered blender (Blendtec or Vitamix type), and blend thoroughly on high power until all corn pieces have been blended into a fine puree. Do this in batches if needed, depending on the size of the blender.

Place cream cheese in a bowl and pour in 1 cup of the blended hot milk mixture; whisk until smooth. Pour in the rest of the mixture as it is blended and whisk to mix well and incorporate the cream cheese.

Pour mixture into a Ziploc bag, sealing in as little air as possible, and submerge in a bowl of ice water until chilled. Place plastic bag in the refrigerator for several hours or, ideally, overnight. Pour mixture into an ice cream maker by cutting off one bottom corner of the bag and squeezing the mixture out. Process according to the instructions provided by the manufacturer of the ice cream maker.

Combine blackberries and sugar in a 1-qt. saucepan over medium-high heat, and cook, stirring, until thick, about 8 minutes; strain and chill.

After churning, alternate layers of ice cream and berry sauce in a storage container before freezing.