Place the figs in a heavy saucepan and cover with the water and sugar. Simmer over medium-low heat, stirring occasionally, until the consistency is jam-like. Remove from heat and set aside.
Combine the cream and walnuts in a small saucepan and bring to boil. Remove from heat and allow the walnuts to steep in the cream for 1 hour. After an hour, stir the cream mixture into the fig mixture, and pour into the bowl of a food processor. Pulse to purée, leaving the walnuts in chunks if you like, or purée until completely smooth. Transfer to a bowl and refrigerate until completely cooled, then freeze in ice cream maker according to manufacturer’s directions. Enjoy!