Step 1: Preheat your oven to 350°F (175°C) and grease an 8×8 inch square baking dish.
Step 2: In a medium bowl, combine the chopped figs, boiling water, and baking soda. Let sit for 15 minutes to soften the figs.
Step 3: In a large mixing bowl, cream together the softened butter and dark brown sugar until light and fluffy.
Step 4: Beat in the eggs one at a time, then stir in the coconut milk.
Step 5: Sift the flour, baking powder, and salt together. Gradually add to the wet ingredients, stirring until just combined.
Step 6: Stir the soaked fig mixture (including the water) and the shredded coconut into the batter.
Step 7: Pour the batter into the prepared baking dish and bake for 40-45 minutes, or until a toothpick inserted into the center comes out clean.
Step 8: While the pudding bakes, prepare the syrup by simmering granulated sugar, 1/2 cup water, and sliced ginger in a small saucepan for 10 minutes. Stir in lemon juice and strain out the ginger.
Step 9: Remove the pudding from the oven, poke holes with a skewer, and pour half the ginger syrup over the top. Serve warm with remaining syrup.