Preheat the oven to 350 degrees Fahrenheit and line an 8-inch square baking pan with parchment paper.

Whisk together the eggs, applesauce, avocado oil, pure maple syrup, and vanilla extract in a large bowl.

Blend the oats in a high-powered blender or a food processor for 60 seconds, or until a flour forms. Add the baking powder, sea salt, and pumpkin pie spice to the blender and blend for another few seconds until the dry ingredients are fully combined.

Pour the dry mixture into the bowl with the wet ingredients and stir well. Stir the chopped apple into the batter.

Transfer the cake batter into the prepared pan and spread it into an even layer.

Bake on the center rack of the preheated oven for 23-28 minutes, or until the cake tests clean.

Insert an instant-read thermometer into the center of the cake to check for doneness. If the internal temperature is 190 degrees F or higher, it is ready.

Allow the cake to cool for at least 20 minutes before slicing and serving. For with a scoop of vanilla ice cream for a decadent dessert, or a cup of coffee as an afternoon snack.