Preheat the oven to 350 degrees F. Grease a 9-inch baking pan or spring-form pan.
Using an electric mixer, beat the butter and 1 cup of the sugar for 3 to 5 minutes on medium-high speed, until light and fluffy.
Add the eggs, one at a time, mixing on low, then the Greek yogurt and vanilla, and mix until the batter is smooth.
In a separate bowl, sift together the flour, baking soda, baking powder, and salt.
With the mixer on low, gradually add the dry ingredients to the wet batter and mix just until just incorporated.
In a small bowl, combine the remaining ½ cup sugar and the cinnamon.
Spread half of the batter evenly in the pan, using a spoon or knife.
Top with half of the peaches, then sprinkle with two-thirds of the sugar mixture.
Spread the remaining batter on top, adding the remaining peaches on top, and sprinkle with the remaining sugar mixture.
Bake the cake for 50 to 60 minutes, or until a toothpick inserted in the center comes out clean. Serve warm or at room temperature.