Whisk 2 tablespoons of the milk with the cornstarch in a small bowl until smooth.
In a medium bowl, whisk the cream cheese and salt together until smooth.
In a measuring cup with a spout, whisk together heavy cream and corn syrup.
Heat the sugar in a large saucepan over medium heat until melted and golden amber in color (see note below). The process happens quickly, so don’t stray to far from the stove. Remove the pan from the heat and, stirring constantly, SLOWLY add a small amount of the heavy cream mixture to the caramel–it will vigorously bubble and spurt, this is normal. Continue to slowly stir in the heavy cream mixture until it’s fully incorporated. A few small chunks of sugar floating around is normal.
Return the pot to medium-high heat and add the milk. Bring the mixture to a rolling boil, and allow the mixture to boil for 4 minutes exactly. Remove from the heat and slowly whisk in the cornstarch slurry.
Return the pot to the heat and bring the mixture back to a boil. Cook, stirring constantly, until slightly thickened, about 1-2 minutes. Remove from the heat.
Slowly whisk the hot milk mixture into the cream cheese mixture until smooth. Whisk in the vanilla extract and bourbon. Strain the mixture through a sieve.
Transfer the mixture to an airtight container. Chill for at least 8 hours, or overnight. Or, if you’re in a hurry, transfer the mixture to a gallon-sized freezer bag and submerge in an ice bath for 30 minutes.
Pour the ice cream base into the frozen bowl of an ice cream maker. Spin until thick and creamy, about 25 minutes. Add a layer of ice cream to the bottom of freezer-safe container with a lid. Sprinkle over a layer of toasted almonds and fudge brownie chunks. Continue to layer until all of the ice cream is transferred over. Cover and freeze for at least 4 hours.