Heat oven to 350°F. Lightly grease the 9x9’’ cake pan.
In a medium bowl whisk together the flour, baking powder, baking soda, cardamom, and salt. Set aside.
In a standing mixer fitted with paddle attachment, beat butter and both sugars on medium speed until light and fluffy, about 2-3 minutes. Next, add egg and mix on medium-low until fully combined.
Add vanilla to container with buttermilk, and gently mix. With the mixer on lowest speed, add flour mixture and buttermilk in three additions, beginning and ending with the flour. After the last addition of the flour, scrape down the sides, then add the walnuts and figs and fold everything together a few times by hand with a spatula.
Pour batter into the prepared pan, and bake for about 35 minutes, or until a toothpick inserted into the center comes out clean. Place the cake on a wire rack and cool completely.
Make the frosting: Beat the yogurt and cream cheese together with a standing or hand-held mixer on medium speed until smooth. Add the powdered sugar, vanilla, and pinch of salt, and continue beating until light and fluffy. Taste and add more sugar if desired.
Once the cake has cooled, top with Greek yogurt frosting and garnish with figs.
Equipment: 9x9-inch cake pan, standing or handheld mixer, medium bowl, whisk, spatula, cooling rack