Preheat your oven to 350°F (175°C).
Grease and line four 8-inch round cake pans with parchment paper.
In a large bowl, whisk together the flour, light brown sugar, granulated sugar, baking powder, baking soda, and salt.
In another bowl, mix the peanut butter, vegetable oil, plant-based milk, dairy-free yogurt, vanilla extract, and apple cider vinegar until smooth.
Add the wet ingredients to the dry ingredients, mixing until just combined. Do not overmix.
Divide the batter evenly among the prepared pans.
Bake for 25-30 minutes, or until a toothpick inserted into the center comes out clean.
Allow the cakes to cool in the pans for 10 minutes, then transfer to a wire rack to cool completely.