Heat the oven to 350°F (177°C) and grease a 9-inch springform pan well. The springform makes release easier, especially with juicy fruit baked into the layers.
Whisk the flour, baking powder, baking soda, and salt in a large bowl until everything is evenly distributed. This dry mix should look uniform with no streaks of leavening left behind.
In a separate medium bowl, whisk the oil, 2/3 cup (133g) sugar, eggs, yogurt, vanilla extract, almond extract, lemon juice, and lemon zest until smooth, then whisk that mixture into the dry ingredients just until combined. The batter should look thick, creamy, and slightly glossy, not lumpy or overworked.
Toss the peach slices with 1 Tablespoon of sugar in a medium bowl, then divide them between two bowls and stir cinnamon into one half. The fruit should be lightly coated and fragrant, with the cinnamon batch evenly dusted.
Spread half the batter into the prepared pan, layer the cinnamon peaches over it, cover with the remaining batter, and finish with the plain sugared peaches on top. Try to keep the layers even so the center bakes through at the same pace as the edges.
Bake for 50–55 minutes, and at about 30 minutes loosely tent the pan with aluminum foil so the top does not brown too quickly. The kitchen will smell warm and peachy, and the cake should look deeply golden by the end.
Check the center with a toothpick, testing more than one spot before pulling the cake from the oven. If one test hits a peach pocket, check again nearby since fruit can make one area look wetter than the cake actually is.
Set the pan on a wire rack and cool the cake for at least 30 minutes before slicing, or let it cool completely, then dust with confectioners’ sugar if desired. The crumb will settle as it cools, making the slices cleaner and easier to lift.
Cover any leftover cake and keep it at room temperature for 2 days or in the refrigerator for up to 5 days. The crumb stays softest when the cake is well covered so it does not dry out.