Combine flours, oats, baking powder and salt in a large bowl; set aside.
In a medium bowl, mash half of a banana (about 1/3 cup) until smooth. Thinly slice the remaining bananas and set aside.
Add the eggs, vanilla, melted butter and milk to the bowl with the mashed banana. Whisk to combine until smooth.
Pour the wet ingredients into the bowl with the dry ingredients and stir until thoroughly combined. Let the mixture sit for 5 minutes while you preheat a large skillet over medium heat.
Once the skillet is hot, add enough butter or ghee to lightly grease the bottom of the pan.
Pour about 1/4 cup batter into the pan and gently press 3 to 4 banana slices onto the top. Once bubbles form on top and the edges are cooked, flip the pancake and cook for an additional 1-2 minutes on the other side until cooked through. If you have a large pan, you can cook multiple pancakes at once.
Keep the pancakes warm on a plate in the oven while you repeat with the remaining batter and bananas using additional butter to grease the pan as needed.