Make the cornstarch slurry:
In a small bowl, combine milk and cornstarch. Stir until completely smooth. Set aside.
Make the caramel:
Before we begin, I must to warn: Making caramel is a dangerous situation. Especially the dry sugar technique. Please exercise caution and ensure you have all the items prepared for this step, as making dry caramel goes quickly and needs to be watched much more closely.
In a small bowl combine the heavy cream, corn syrup, and sea salt. Set aside.
Sprinkle sugar in one even layer over a 4-quart saucepan. Turn the heat to medium and allow the sugar to melt. When the edges of the sugar begin to melt and darken, using a heatproof spatula, quickly begin pushing the melted sugar towards the center of the pan to help it all melt. Continue pushing the edges this way until all the sugar has melted evenly and is a nice amber color. What you’re looking for is the color of an old penny. Once this color is achieved, quickly remove from the heat and immediately, yet very slowly pour the heavy cream/corn syrup/salt mixture into the melted sugar. Be sure to stand back. This will bubble, pop, spit at you and generally try to suck you into a caramel dimension. Still until it’s all incorporated. Set aside momentarily.
Make the ice cream:
Whisk the cream cheese and vanilla extract in a large sized bowl until smooth and set aside. Fill a large bowl with ice and water and place an open 1 gallon Ziploc bag inside the ice water. Also set aside.
Return the pan with caramel back to the stove. Add the milk and sugar. Stir to incorporate. Over medium/high heat bring the mixture to a full simmer, about 3-5 minutes. Make sure to watch it so it does not spill over. Gradually whisk in the cornstarch slurry and cook the mixture whisking the entire time until slightly thickened, about 2-3 minutes. Remove from heat. If any caramel flecks remain, strain the mixture to remove.
Gradually add the caramel base into the cream cheese and whisk vigorously until very smooth. Slowly pour the mixture into a 1-gallon Ziploc freezer bag and seal. Submerge the sealed bag in the ice water bath. Let stand, adding more ice as necessary, until cold, about 30 minutes. Place in the refrigerator to cool and steep for at least 2 more hours.
Once the mixture has finished steeping, pour into an ice cream maker and freeze according to manufacturer’s directions. Once frozen, fold in the pretzel pieces and pour ice cream into a container with an airtight lid. Store in your freezer until firm, about 4 hours.
Makes just about 1 quart of ice cream.