Using 2 forks, shred ham into bite-size pieces. (You should have 1 cup.)

In a saucepan, melt butter over medium heat. Add shallot and cook, stirring occasionally, until softened, about 3 minutes. Stir in ham. Increase heat to high and add cider; cook, stirring occasionally, until liquid is reduced by half, about 3 minutes. Reduce heat to medium, add cream, and heat through, stirring often, until just bubbling, 5 to 6 minutes.

Stir in oysters and liquor; cook until oysters turn opaque and begin to curl, 1 to 2 minutes. Lightly season with salt and pepper. Divide among 4 bowls and serve, with crackers and more pepper.