In a large bowl, combine the flour and baking powder. Set the bowl aside.
In another bowl, beat the eggs, sugar, and vanilla for about 5 minutes with an electric mixer. At low speed, add half the milk, and then incorporate the dry ingredients. Add the remaining milk and whisk until the batter is smooth. Let the batter rest for 10 minutes at room temperature.
Place a non-stick skillet over medium heat. When the skillet is hot, brush it with butter. Be careful not to burn yourself.
For each pancake, pour about 75 ml (1/3 cup) of batter into the centre of the skillet. With the back of a spoon, lightly spread the batter.
Cook the pancake for 1 to 2 minutes on each side. It is ready to be flipped when bubbles appear in the centre or the edges appear drier. Adjust the heat, if needed, to give the batter time to cook before it browns too much.
Keep the pancakes warm while preparing the remaining pancakes or serve them as you cook them. Delicious with maple syrup or blueberry sauce.