Adjust oven rack to middle position and heat oven to 350 degrees. Grease 6-inch round cake pan. Combine 2 tablespoons granulated sugar and cinnamon in medium bowl. Measure out and reserve 1 tablespoon cinnamon sugar. Add peach wedges to bowl with remaining cinnamon sugar and toss to coat; set aside.
Whisk flour, baking powder, and salt together in medium bowl.
Whisk oil, brown sugar, egg, milk, vanilla, and remaining 2 tablespoons granulated sugar in separate bowl until combined, then stir milk mixture into flour mixture until just combined.
Transfer batter to prepared pan, smooth top, and gently tap pan on counter to release air bubbles. Arrange reserved sugared peach weages in pinwheel pattern in cake batter, then sprinkle reserved 1 tablespoon cinnamon sugar mixture evenly over peaches.
Bake until top of cake is golden brown and toothpick inserted in center comes out with few moist crumbs attached, 30 to 40 minutes, rotating pan halfway through baking.
Let cake cool in pan on wire rack for 20 minutes. Remove cake from pan and let cool completely on rack, about 1 hour. Serve.
This cake is unmistakably summer, with a pretty peach pinwheel pattern on top, and it's so simple to make the perfect dessert on a lazy late-season day. For an ultramoist cake, we opt for vegetable oil instead of butter; unlike butter, oil doesn't solidify at room temperature after the cake is baked and cooled. Using vegetable oil also eliminates the need for a mixer.
We scrape the batter into a 6-inch cake pan and arrange peach slices that have been rolled in cinnamon sugar on top. Since overly ripe peaches will make the cake soggy, we recommend using a barely ripe peach, one that gives only slightly to the touch. L.I.
