Step 1: Place whole tangerines in a pot of water and boil for 1 hour until very soft. Drain and let cool.
Step 2: Once cool, cut tangerines in half and remove any seeds. Place the whole fruit (including peel) in a food processor.
Step 3: Add the chopped dates to the food processor and pulse until you have a thick, relatively smooth paste.
Step 4: In a large bowl, whisk the eggs and 1 cup of sugar together until pale and slightly thickened.
Step 5: Fold the tangerine-date puree into the egg mixture until well combined.
Step 6: Gently stir in the almond flour, baking powder, and salt until a cohesive batter forms.
Step 7: Pour the batter into a greased 9-inch springform pan and bake at 350°F (175°C) for 45-50 minutes.
Step 8: While the cake bakes, combine 1/2 cup water, 1/2 cup sugar, and crushed cardamom pods in a small saucepan.
Step 9: Simmer the syrup for 10 minutes, then strain and let it cool slightly.
Step 10: Poke holes in the warm cake with a skewer and pour the cardamom syrup over the top. Let cool completely before serving.