Preheat the oven to 190c/170c (fan)/gas 5. Butter a 33 x 23 x 8cm baking tin and line the bottom and sides with parchment paper.
First make the crumble. Put all the ingredients into a food processor and pulse until the size of large breadcrumbs. Do not overmix or it will turn into a wet dough. Alternatively you can mix it by hand with a pastry cutter or back of a fork. Cover and place in the fridge until ready to use.
Now make the bun. In a small pan, melt the butter and leave to cool slightly. In a large bowl, whisk together the flour, baking powder, salt and caster sugar.
In a separate bowl, whisk together the eggs, vanilla and yoghurt. Now slowly drizzle the melted butter into the yoghurt mixture, whisking constantly to emulsify. Make a well in a dry ingredients and pour the wet ingredients. Stir together gently until just combined. Pour into your prepared baking tin and set aside.
Slice the peaches into eighths or sixteenths, depending on their size, and scatter them randomly over the batter. Cover the fruit with the crumble mixture and bake for about 1 hour, until an inserted skewer comes out clean. Test for doneness. The crumb should be tender, not dry, but neither should it be wet. Allow to cool for 15 minutes before cutting into slices and serving.