Place the dates, dried figs and 2 cups water in a medium saucepan and bring to boil over moderate heat. Remove the pan from the heat and stir in the baking soda. Let cool for about 15 minutes, before adding to a blender and pureeing until smooth.
Cream the butter and sugar in a large bowl, until fluffy, about 3 minutes. Add the eggs and beat until well combined. Fold in the flour and the pureed fig mixture. Stir in the chocolate chips. Pour the batter into a greased 6-qt glass heat-proof bowl with butter or baking spray.
Insert a metal trivet into the Instant Pot and pour in the remaining 1 ½ cups water. Place the bowl with the batter into the Instant Pot and lock the lid in place, making sure the valve is set to seal. Pressure cook on high for 40 minutes, allowing to natural release for 10 minutes before manually releasing any remaining pressure.
Carefully open the lid and transfer the pudding bowl to a wire rack to cool. Remove the metal trivet and discard the water. Wipe the inner bowl dry and set to sauté. Once hot, add the brown sugar, cream and butter. Cook, stirring often, until the sauce has thickened, about 8 minutes. Turn the machine off and stir in the vanilla, bourbon (if using) and salt.
Invert the figgy pudding bowl onto a platter and slice. Serve with the warm sauce and a dollop of cream.