Preheat oven to 350°F / 175°C and lightly grease your doughnut pan(s).
Combine all wet ingredients (Greek yogurt, egg, egg yolk, vanilla, oil) and sugar, cardamom, cinnamon, and salt and mix thoroughly to combine.
Add flour and baking soda and mix gently until just combined, add blueberries and mix gently until evenly distributed. Spoon into the doughnut cavities – being sure not to fill more than half way.
Bake for 12-16 minutes, or until the tops are firm and golden. Do not attempt to flip during cooking.
Allow to cool on a wire rack for 30 minutes before icing.
For the Icing:
Combine icing sugar, jam, and water and mix to combine. The mixture should be thick, but still viscous / (slow) pourable.
Dip each doughnut light side down into the icing and then set on to your cooling rack. You can dip again if you prefer more icing. Serve immediately.