Position a rack in the middle of your oven and preheat it to 350°F. While it heats, generously grease a 9x13 inch baking dish or similar size cake pan with butter or oil, making sure to coat the bottom and all sides evenly. This prevents sticking and ensures even browning on the edges.
In a large mixing bowl, whisk together the room temperature eggs, vegetable oil, both sugars, water, and vanilla extract until well combined and slightly emulsified. The mixture should look smooth and slightly pale—this typically takes about 1-2 minutes of whisking. Having your eggs at room temperature helps them incorporate better into the oil, creating a more cohesive batter.
In a separate bowl, whisk together the 2 cups flour, 2 tsp baking powder, 3/4 tsp salt, and freshly ground cardamom. I prefer using freshly ground cardamom here because it has significantly more aromatic punch than pre-ground. Now fold the dry ingredient mixture into the wet batter from Step 2 using a spatula, stirring just until combined—don't overmix, as this keeps the cake tender. Gently fold in the finely minced candied ginger and lemon zest, distributing them evenly throughout the batter.
In a separate bowl, combine the 1/2 cup flour, 1/2 tsp baking powder, 1/4 tsp salt, 2 tbsp sugar, 2 tbsp brown sugar, and cinnamon. Cut the cold butter into small cubes and add it to the dry mixture, then use your fingertips to rub the butter into the flour until the mixture resembles coarse breadcrumbs with some pea-sized butter pieces remaining. Stir in the coarsely chopped walnuts, breaking up any clumps.
Pour the batter from Step 3 into your prepared pan, spreading it evenly. Distribute the stemmed and quartered figs evenly across the top of the batter—they'll partially sink in as the cake bakes, creating pockets of fruit throughout. Sprinkle the crumble topping from Step 4 evenly over the entire surface, gently pressing it down slightly so it adheres to the batter but doesn't compress too much. Place the pan in the preheated oven and bake for 50 minutes, or until a toothpick inserted into the cake (avoiding the figs) comes out clean or with just a few moist crumbs.
Remove the cake from the oven and let it cool in the pan for at least 15 minutes before cutting. This resting time allows the structure to set properly so it slices cleanly. Serve warm or at room temperature—the flavors actually develop nicely as it cools.