Step 1

Prepare an ice bath in a large bowl with water and ice. Stir 1/4 cup of milk and the cornstarch in a bowl to create a slurry and set aside.

Step 2

In medium saucepan over medium-high heat, whisk the remaining milk, cream, sugar, corn syrup, and salt together. Bring to a boil, then cook for 4 minutes.

Step 3

Whisk in the cornstarch and milk slurry, then bring to a boil again, cooking and stirring for 2 minutes until thickened.

Step 4

Place the cream cheese in a large bowl. Add 1/4 cup of the hot liquid and whisk until smooth. Whisk in remaining milk mixture. Stir in graham cracker crumbs and vanilla. Pour into plastic bag and submerge in ice water until chilled.

Step 5

Pour into ice cream maker and churn according to manufacturer's instructions.

Step 6

Stir in graham cracker pieces, honeycomb candy, and mini chocolate chips, then pour into containers and freeze 4 hours to cure.