1. Make the molasses curd: Preheat the oven to 300 degrees.
In a large bowl, whisk eggs until slightly frothy, then add brown sugar, molasses, dark rum, salt, and vanilla, and whisk well to combine. Pour mixture into a 9-inch square baking dish and bake for 30 to 35 minutes, rotating the dish halfway through, until edges are set, but center jiggles slightly; do not overbake. Let cool completely on rack, then refrigerate. Measure out a ½ cup of molasses curd and reserve the rest for another use. Place canister for ice cream maker inside the freezer to chill.
2. In a small bowl, mix about 2 tablespoons whole milk with cornstarch to make a smooth slurry. In a medium bowl, whisk cream cheese and salt until smooth. Fill a large bowl with ice and water.
3. 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 gradually whisk in the cornstarch slurry. Bring mixture back to a boil over medium-high heat and cook, stirring with a heatproof spatula until slightly thickened, about 1 minute. Remove from heat.
4. Gradually whisk hot milk mixture into cream cheese until smooth. Pour mixture into a 1-gallon Ziploc freezer bag and submerge sealed bag in the ice bath. Let stand, adding more ice as necessary, until cold, about 30 minutes.
5. Remove frozen canister of ice cream maker from freezer. Assemble ice cream machine and turn it on. Pour the ice cream base into canister and spin until thick and creamy.
Pack the ice cream into a storage container, layering it with the molasses curd and peanuts. Drizzle a spoonful of the curd onto the bottom of a storage container, sprinkle in peanuts, and spread a layer of ice cream over it. Add a few more spoonfuls of curd and peanuts into the nooks of the ice cream, and then add another ice cream layer. Continue layering sauce, peanuts, and ice cream layering until all ice cream is used. The sauce should not cover the whole layer. Note that you do not want to swirl in the sauce because it will get lost in the ice cream.
6. Press a sheet of parchment directly against the surface, and seal with an airtight lid. Freeze in coldest part of freezer until firm, at least 4 hours.