Preheat the oven to 350℉. Grease a loaf pan and line the bottom with parchment paper.
In a large bowl, rub the zest of ½ teaspoon ground cinnamon into the 1 cup brown sugar, then whisk in the ½ cup Greek yogurt, 3 large eggs, and 1 teaspoon pure vanilla extract, stirring and whisking until well blended. Add the 1 ½ cups oat flour, ¼ cup almond flour, 2 teaspoons baking powder, ½ teaspoon ground cinnamon½ teaspoon ground ginger, and ¼ teaspoon fine sea salt, mixing just to combine. Add the ½ cup oil and stir well to incorporate. Fold in the 1 ½ cups chopped peaches. Keep stirring until it forms a smooth batter. Pour and scrape the batter into the prepared pan.
Rest the batter while the oven heats, then place in the oven and bake for 30-40 minutes until a toothpick inserted into the center comes out clean. Do not overbake.
Cool cake on a rack for about 20 minutes; then turn it out of the pan to cool completely before slicing.
Notes
Fresh but not overly soft peaches. You don't want the peaches to completely disappear into the batter, so skip the super soft peaches (these are great for draping over a bowl of Greek yogurt and drizzling with honey, eaten over the kitchen sink, or cooked into peach butter). Still, you do want to use peaches that are ripe. So choose peaches that are just slightly soft when pressed.
To peel or not to peel. I'll confess that a lot of the time, I don't peel my peaches before adding them to the batter. For one thing, it's a hassle. And for another, I doubt anyone can tell if the peel is left on! Just give the peaches a good wash before prepping them if you leave on their skins.
Cut into small pieces. This means bite-size, or approximately (about ½-inch pieces). This will help the peaches to meld into the batter.
No need to toss peaches with flour. Some recipes recommend tossing fruit with flour first before folding it into a batter. I don't find that this makes much of a difference here, so I skip this step.
It may take a bit longer to bake. Note that the 55 minutes of baking time may go a tad longer because of the moisture content in the peaches. Just keep checking every 5 minutes or so after 55 minutes until done.
Cool completely. I advise this with every gluten-free bake, and especially here because the peaches can make the warm loaf even more delicate. Make sure to let the bread cool completely before slicing so that it doesn't fall apart.