Mix about 2 tablespoons of milk with the cornstarch in a small bowl to make a smooth semi-liquid mixture. In a medium bowl, mix the cream cheese and salt together with a spatula.
Combine the remaining milk, cream, sugar and corn syrup in a 4-quart saucepan. Bring to a boil over medium high heat and boil for 4 minutes. Remove from heat and whisk in the cornstarch slurry. Bring the mixture back to a boil over medium-high heat and cook, whisking until thickened (about 1 minute) and remove from heat.
Whisk hot mixture into the cream cheese mixture, then stir in the broken Annie’s Honey Bunny Grahams. Allow the mixture to steep for about 3 minutes, or until the Bunny Grahams dissolve. At this point, beat with an electric mixer or puree with an immersion blender. Next, force the mixture through a fine mesh strainer into a clean bowl. Whisk to cool a bit. Cover with plastic wrap and place in the fridge to chill for 5 hours, or until cooled completely.
To make the French silk pie filling, fit a stand mixer with the whisk attachment and cream the butter. Slowly add sugar and whip until smooth. Blend in chocolate until mixed evenly. Add eggs, one at a time, beating 5 minutes after each. (Tip: This step is a must! Skimping on the time will yield a runny mixture.)
Next, add vanilla and mix until combined, scraping the sides. Place mixture in the fridge until you’re ready to churn the ice cream.
Churn Honey Bunny Ice Cream in your ice cream maker according to the manufacturer’s directions. Layer in storage containers with French silk pie filling, Honey Bunny Grahams, and creme filled chocolate cookies. Cover with plastic wrap and seal with an airtight lid. Freeze until firm, at least 4 hours.