Preheat the oven to 175°C (350 °F) and line the bottom of a springform pan with parchment paper. Wash the grapes, pat them dry, and remove them from the vine. Cut big ones in half.
Mix the spelt flour with baking powder, baking soda, and a pinch of salt in a bowl.
Whisk together the brown sugar, eggs, vanilla extract, cardamom, vegetable oil, and yogurt in another bowl.
Sift the flour mixture into the wet ingredients and whisk until smooth without lumps.
Slightly coat the grapes in flour and fold them into the dough. Transfer the dough to the baking pan. Scatter over some more grapes and bake in the oven for 45-50 minutes, until a toothpick inserted into the dough comes out mostly clean.
Take the cake out of the oven and let it cool in the baking pan. Then, remove the cake from the pan, sprinkle the cake with powdered sugar if you like, and serve.