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