Heat oven to 350°F. Grease 9-inch springform pan lightly with baking spray or oil, and line the bottom with parchment.
Roughly chop peaches. Should have about 3 cups.
Whisk together yogurt, olive oil, sugar, eggs, and vanilla. Add flour, baking powder, baking soda, salt, ginger, cloves and nutmeg to liquid mixture and stir just until no large lumps remain. Fold in chopped peaches.
Pour batter into cake pan and bake for 50 to 60 minutes, covering with foil near end of cooking if top is browning too much. When tester comes out clean, transfer cake to cooling rack and let it cool for 10 minutes before removing from pan.
For cinnamon glaze: whisk together ingredients. Thin, if necessary, with water.
Place on plate, drizzle with cinnamon glaze. Garnish with toasted hazelnuts.
Serve cake warm or at room temperature. When well-wrapped, this keeps very well for several days.