How to Make It
In a small heatproof bowl, soak the figs in boiling water until softened, about 20 minutes. Drain the figs and pat dry. Slice off the tough stems, then cut the figs into 1/2-inch dice.
In a food processor, combine the flour, butter, Cheddar cheese, kosher salt and pepper and pulse until the mixture resembles coarse meal. Scrape the mixture into a large bowl and add the figs and egg. Using your hands, work the dough until it comes together.
Scrape the dough onto a large piece of plastic wrap and pat it into a 12-by-2-inch rectangular log. Wrap the log tightly and refrigerate until firm, at least 1 hour, or overnight.
Preheat the oven to 375°. Butter 2 large baking sheets. Slice the log of dough crosswise 1/4 inch thick. Arrange the slices at least 1 inch apart on the prepared baking sheets. Bake the Cheddar crackers for about 12 minutes, or until they are golden brown and slightly firm. Carefully transfer the crackers to a wire rack to cool.