Preheat oven to 375°F with rack in middle. Line the bottom of a 9x3-inch springform pan with parchment paper. Grease the side of the pan with butter or cooking spray.
Combine flour, baking powder, baking soda together in a medium bowl.
In a small bowl, combine 1 teaspoon chia seeds and 3 teaspoons hot boiling water. Mix and let it sit for a couple of minutes until a slurry forms.
In a separate bowl, beat butter and sugar until light and fluffy. Add vanilla and 2 eggs and continue beating until very creamy and light in color. Add chia seeds slurry and beat to combine. Add greek yogurt and beat to combine.
Keeping the mixer speed low, mix in the combined dry ingredients from step 2 into the wet ingredients, in 3 separate batches until all incorporated.
Transfer the cake batter to the springform pan. Place sliced peaches evenly on top, reserving about 10 slices.
Bake until cake turns golden, and the tester comes out clean, about 20 to 35 minutes, depending on your oven. 15-20 minutes into baking, when the cake rises but is still not browned on top, carefully take it out the oven and carefully arrange the reserved 10 peach slices on top. Return to the oven and bake for 5 to 15 more minutes.
When the cake is done baking, let it cool (still in the baking pan) on a wire rack. After cake has cooled for about 40 minutes, release the cake from the springform pan. At this point, if the cake is cool enough, you can slide your hand under the cake, between the parchment paper and the bottom portion of the springform pan and move the cake with the parchment paper attached to its bottom onto a cake plate easily.