Put the 1 cup of milk and 1 cup of the cream into a heavy saucepan (2 quart). Add the allspice, and a pinch of salt and heat until steamy, but not boiling. Lower the heat to warm, cover, and let spices steep for at least a half hour. Add the sugar and stir until it is completely dissolved.
Put remaining 1 cup cream in a metal bowl, resting in a larger bowl of ice water. Place a fine mesh strainer over the bowl of cream.
Whisk the egg yolks in a medium sized bowl. Slowly pour about half of the heated cream milk mixture into the egg yolks, whisking constantly so that the egg yolks are tempered by the warm mixture, but not cooked by it. Scrape the warmed egg yolks back into the saucepan.
Return the saucepan to the stove on medium heat, stirring the mixture constantly with a wooden spoon, scraping the bottom as you stir, until the mixture thickens and coats the spoon. You should be able to run your finger across the coating and have the coating not run. This can take about 10 minutes. The second this happens the mixture should be removed from heat immediately, and poured through the sieve over the ice bath to stop the cooking.
Pour the custard through the strainer (from step 2) and stir into the cold cream to stop the cooking. Once initially chilled in the ice bath, chill the mixture thoroughly in the refrigerator (at least a couple of hours). It should be noted here that if you choose to not use the alcohol it will affect the texture of your ice cream by making it "icier".
When it comes time to churn the ice cream, stir in the vanilla extract and the rum, bourbon, or brandy. Then process the mixture in your ice cream maker according to the manufacturer's instructions. (I used my kitchenaid.)
Remove ice cream from the ice cream maker and transfer it to an airtight container; store in your freezer for several hours before eating. Note that the ice cream will be quite soft coming out of the ice cream maker. It will continue harden in your freezer. If stored for more than a day, you may need to let it sit for a few minutes to soften before attempting to scoop it.