In a spouted mixing bowl, whisk together the cornstarch, ¼ cup (50g) of the sugar, milk powder, salt, eggs, yolks, and ¼ cup (60g) of the milk until smooth. Set aside.
In a large saucepan, combine the remaining 2 ¾ cups (660 grams) of milk and the remaining sugar (125 grams). Set over medium heat and cook, whisking, until very hot and just beginning to bubble.
Gradually whisk the hot milk mixture into the egg mixture. Return everything to the saucepan and cook over medium heat, stirring constantly, until slightly thickened and the mixture reaches 170°F.
Remove from heat and strain into a clean bowl. Stir in cream, honey and vanilla.
Let cool slightly at room temperature, then cover and chill for several hour or until very cold.
To quick cool, pour mixture into a heavy duty zipper bag and submerge in ice water for about 30 minutes.
Once the custard mixture is very cold, stir in the vodka. Process in an ice cream maker according to manufacturer’s instructions.