Preheat Oven to 350° F (180° C). Lightly spray a 9-inch springform pan with cooking spray and place a piece of parchment paper on bottom. Follow by lining the sides with strips of parchment paper as well. This allows for easy removal of the finished cake from the pan.
The Crumb Topping: In a small bowl, whisk together all the dry ingredients, then add the melted butter. Using your fingertips, massage the ingredients together until they form medium-large crumbs. The mixture will be slightly wet but will firm up as the butter cools and absorbs into the flour while you prepare the other components.
The Caramelized Peaches: Rinse the peaches and slice them into ½-inch wedges, leaving the skin on. Set aside. In a 10-inch skillet over medium heat, combine the sugar, cinnamon, nutmeg, and lemon juice. While stirring, cook until the sugar has dissolved. In a small bowl, whisk together the cornstarch and water, then add it to the skillet. Stir gently for about 2 minutes, until the juices have thickened. Remove from heat and stir in the vanilla to preserve its flavor. Add the sliced peaches to the thickened sauce and gently coat them. Set aside to cool.
Make the Cake Batter: In a large mixing bowl, beat the eggs and sugars with a hand mixer until light in color. Add the olive oil, sour cream, milk, and vanilla, and beat on low speed until well combined.
Sift: Through a sieve, sift all the dry ingredients into the wet mixture, then gently fold them in with a silicone spatula until the flour disappears into the batter—similar to pancake batter. A few small lumps are fine. Do not overmix to avoid a dense cake.
The Cinnamon Ripple: In a small bowl, stir together the brown sugar and cinnamon until well combined.
Assembly for Baking: Pour half the cake batter into the prepared springform pan, then evenly sprinkle the cinnamon ripple on top. Arrange the caramelized peaches in an even layer over the ripple. Dollop the remaining batter on top and spread it evenly. Finish by sprinkling the crumb mixture over the top.
Bake: Bake for 60 minutes, until the crumb topping is a deep golden brown. Test with a long toothpick or cake tester inserted into the center. If it pulls out with light moist crumbs, the cake is done. (I prefer a toothpick, as cake testers can be too fine and may come out clean, making it harder to judge.)
Prepare the Streusel: While the cake is cooling, whisk together the powdered sugar, milk, and vanilla in a small bowl. The glaze should be thick and white, but thin enough to drizzle. Adjust the liquid as needed to achieve your desired consistency. Allow the cake to cool for 15 minutes before drizzling to maintain a bright white contrast.
Enjoy! Let the cake cool for 30-40 minutes and enjoy while warm! Serve with extra caramelized peaches or a scoop of vanilla ice cream. Store leftovers in an airtight container in the fridge for up to 2 days.