Preheat the oven to 350°F (175°C). Grease and flour a 9-inch round cake pan.
In a large mixing bowl, cream together the softened butter and granulated sugar until light and fluffy.
Beat in the eggs, one at a time, followed by the vanilla extract.
In a separate bowl, whisk together the flour, baking powder, baking soda, and salt.
Add the dry ingredients to the wet ingredients in three additions, alternating with the milk. Mix until just combined.
Gently fold in the chopped figs and walnuts.
Pour the batter into the prepared cake pan and smooth the top.
Bake for 40-45 minutes, or until a toothpick inserted into the center comes out clean.
Allow the cake to cool in the pan for 10 minutes, then transfer to a wire rack to cool completely.
Serve and enjoy!