To mix the cake: In a large mixing bowl, whisk the eggs, yogurt, oil, sugars, and vanilla until combined.
In a small bowl, mix the flour, baking powder and salt.
Add the dry ingredients to the wet ingredients and mix to combine, without over mixing. See photos above. Over mixing can results in a dry, tough cake. A few small lumps are okay.
In a separate bowl, combine the peaches with the sugar.
In another bowl, mix the oats, sugars, flour, cinnamon, and butter until you have a well combined mixture.
To bake the cake: Add half of the batter to the cake pan and smooth it out. Layer half of the peaches. Repeat with the rest of the batter and peaches. Top the peaches with the oat crumble mixture. Bake for about 60 minutes or until a toothpick comes out clean.
Let cool completely in the cake pan if you want to be able to slice the cake.
If you want it warm, the cake will be looser but will go well with vanilla ice cream.
Notes
I always weigh my flour. Your results should be like mine if you weigh. If you scoop, you may add too much flour, resulting in a more dense cake.Substitutions: Greek yogurt: Sour cream should be fine. Just avoid non-fat options. Oil: Use any neutral oil like canola, sunflower, or light olive oil (not extra virgin).Storage:Store leftover peach crumble cake in an airtight container at room temperature for up to 2 days. If your kitchen is warm or humid, keep it in the fridge instead to help it stay fresh.