In a large skillet cook the onions with 1/4 cup of the chicken or duck fat, stirring frequently, until they are browned and beginning to caramelize. It will take 10 to 15 minutes. Once browned, scrape them onto a paper towel-lined plate and let them drain.
Add the chicken livers to the pan and season with the salt and pepper. Cook the livers, stirring often, until they are just-cooked through but still pink inside. Remove from heat.
In a food processor, pulse the hard-boiled eggs a few times, then add the cooked livers (scraping in any pan juices), vinegar, liquor, cayenne, the fried onions, and the remaining 1/2 cup melted chicken or duck fat, then puree until smooth. Taste, and adjust with salt and pepper. (In the app, Michael Ruhlman suggests that if you want it very smooth, you can press the mixture through a wide mesh sieve. I didn’t do that as I didn’t want to lose any of those little caramelized bits of onion.)
Scrape the mixture into a pâté mold or decorative bowl, and chill a few hours, until firm.
To make the jelly, put the water and 2 tablespoons of the port in a small bowl and sprinkle the gelatin over it. Let sit 5 minutes.
In a small pan, warm the 1/2 cup of the port with the sugar, allspice, then pour it over the softened gelatin, stirring until the gelatin is completely dissolved. Let the mixture cool until it’s tepid, then pour it over the back of a spoon (to avoid creating a divot in the pâté), over the chilled pâté.