Preheat the oven to 350°F (175°C). Grease a 9×13-inch baking pan with cooking spray or olive oil.
In a small bowl, combine softened butter, brown sugar, and 2 teaspoons cinnamon until the mixture resembles wet sand.
Peel, core, and dice the apples into approximately ½-inch pieces.
In a large bowl, whisk together sugar, yogurt, olive oil, eggs, vanilla extract, and salt until smooth.
Fold the diced apples into the wet mixture.
Add flour, remaining cinnamon, nutmeg, baking powder, and baking soda. Stir gently until just combined. Avoid overmixing to keep your Apple Yogurt Cake light and tender.
Spread half the batter into the prepared pan.
Sprinkle half of the cinnamon sugar mixture evenly over the batter.
Cover with the remaining batter and finish with the remaining cinnamon sugar mixture.
Bake for 40–45 minutes, or until a toothpick inserted into the center comes out clean.
Cool in the pan for at least one hour before slicing and serving warm or at room temperature.