In a bowl mix together flour, baking powder, brown sugar, baking soda, salt and nutmeg.
In another bowl mash together the bananas. Whisk in eggs, milk, cooled butter, and vanilla.
Pour wet mixture into dry mixture until stir until fully incorporated - do not overmix batter. Let it sit for 5 minutes.
Set a griddle or nonstick pan over medium heat until hot.
Place a tablespoon of butter and vegetable oil on the pan and mix together. Pour 1/4 cup of batter onto pan. Repeat with batter so you have 2-3 pancakes on pan.
Cook until a few bubbles form on top of each pancake and the underside is golden brown, about 2 minutes. Flip the pancakes and cook until golden, 1-2 minutes.
Wipe pan clean with paper towels and add more oil and butter. Repeat this until you've used up all of the batter.
Serve pancakes with syrup and butter.
Notes
Once the pancakes cool, you can freeze the pancakes by putting on a parchmnet lined baking sheet. After they are completely frozen put in freezer bags to store. When you are ready to eat put in toaster to thaw.