Beat the cheese and butter until creamy. In a separate bowl combine the flour, cornstarch, salt and pepper and walnuts.
Stir the dry ingredients into the cheese and butter and mix well. Roll dough into two inch diameter tubular round logs, wrap in plastic and chill until firm. Cut chilled logs into ¼ inch slices. Place shortbread discs on a cookie sheet lined with parchment paper.
Bake at 375 degrees for 10-12 minutes, until golden.
Put all ingredients in a small saucepan and bring to a simmer. Cook for 10-12 minutes and then turn off heat. Cover with a lid.
When figs are cooled off pulse in a food processor.
Top each shortbread with a dollop of compote and serve.