Step 1: Preheat your oven to 350°F (175°C) and grease a 9-inch round cake pan or line it with parchment paper.
Step 2: In a medium bowl, whisk together the all-purpose flour, finely ground pistachios, baking powder, ground cardamom, and salt.
Step 3: In a large bowl, cream the softened butter and sugar together until the mixture is light, pale, and fluffy.
Step 4: Add the eggs one at a time, beating well after each addition to ensure a smooth batter.
Step 5: Stir in the Greek yogurt, vanilla extract, and rose water until fully combined.
Step 6: Gradually fold the dry ingredients into the wet ingredients using a spatula until just combined; do not overmix.
Step 7: Pour the batter into the prepared pan and smooth the top with a spatula.
Step 8: Bake for 40-45 minutes, or until a toothpick inserted into the center comes out clean.
Step 9: Allow the cake to cool in the pan for 10 minutes before transferring it to a wire rack to cool completely.
Step 10: Once cooled, garnish with dried rose petals and extra crushed pistachios before serving.