Closely adapted from Sabrina Ghayour. The original recipe calls for fine ground polenta--I could not find any plain polenta let alone a particular grind. The cornmeal selection was not great either. I finally settled for instant polenta, so I am calling for instant polenta as I cannot be sure if my recipe has enough liquid for non-instant.
Melt the butter and set it aside to cool.
Bring a deep pot of water to a boil and add the peaches. Simmer for about 25 minutes, until the peaches are soft. In the meantime, have a bath of ice water ready for the peaches.
Drain the peaches and then drop them into the prepared ice water bath.
Carefully slice the peaches to remove the pits and then place them in a blender. Puree until smooth.
You should have 1 3/4 cups of peach puree. Set it aside.
Preheat the oven to 350 F. Grease a 9-inch springform pan and then line the bottom with a circle cut out of parchment paper. Lightly grease the parchment paper as well and be sure the sides of the springform pan are extra well greased.
Beat the sugar and eggs together in a large bowl with a flat whisk. Zest the limes and reserve about a teaspoon of it for topping the cake. Whisk the rest of the zest into the sugar and eggs.
Switching to a silicone spatula, mix the blitzed pistachios and polenta into the eggs and sugar. Then fold the melted and cooled butter into the mixture. Last fold in the peach puree.
Pour the batter into the prepared pan. Bake for 45-50 minutes, or until a cake tester inserted into the center of the pan comes out clean.
Let the cake cool completely in the pan. Then use a slim knife to run along the edges of the cake to make sure it does not stick to the pan when you release the springform.
If you think the entire cake will be eaten in one setting, feel free to garnish the entire cake at once. But for us it made more sense to garnish individual slices. Some of us preferred the cake plain and some of us (me!) adored it with the tangy garnish.
Whisk together the first 5 ingredients of the topping. You can store this in the fridge in an airtight container and drizzle it over the cake whenever you want a slice. Then layer a few slices of a peach over the yogurt--white peaches were tastier this year in my neck of the woods, so I used them for the cake, but yellow peaches are so much more visually dramatic, so I used them for the topping. Sprinkle the whole thing with chopped pistachios.
*I used an Icelandic yogurt because that is what I had. Most importantly, use a thick yogurt (either Greek or Icelandic most probably) that is whole fat.
**I recently discover local spring honey, the honey made from the flowers in the spring and could not believe how much more I loved it as compared to clover honey (which is what is usually sold in stores and is made in the summer). Obviously use any honey that tastes good to you.