Make the syrup at least a day ahead. When ready, bring 3 cups water, sugar, honey, and cardamom to a boil in a medium heavy saucepan, stirring until sugar dissolves. Reduce heat to medium-low; simmer, and syrup is reduced to 3 1/4 cups, about 40 minutes. Strain syrup, removing cardamom pods and seeds.
When ready to make the cake, first, preheat oven to 350F, then brush 9" diameter springform pan with oil.
Have two medium bowls and one large bowl set aside. In the first medium bowl, whisk both flours and the baking powder, ground cardamom, salt and baking soda. Mix well.
Using an electric mixer with the large bowl, beat 1/4 cup sugar and 1/2 cup oil for 1 minute. Beat in yolks, then add the flour mixture. Beat in yogurt, zest, and extracts.
In the other medium bowl and using clean, dry beaters, beat egg whites until soft peaks form. Gradually beat in remaining 1/4 cup sugar until firm peaks form. Fold egg whites into batter just to blend, in 2 portions. Transfer to prepared pan and smooth the top.
Bake cake until a toothpick inserted into center comes out clean, about 25 minutes. Pierce hot cake all over with a thin metal skewer. Slowly drizzle 3/4 cup warm syrup all over. When syrup is absorbed, slowly pour 3/4 cup more syrup over. Reserve remaining syrup to use during serving.
Let cake cool in pan on a wire rack. Run a thin knife around edge of pan to release cake. Remove pan sides. Sprinkle almonds over. Cut into wedges and serve drizzled with more syrup.