Separate the eggs, placing the whites in a clean bowl. Place the egg whites in the freezer for about 15 minutes while you prepare the yolk batter.
Whisk the egg yolks, milk, and vanilla together until smooth and slightly frothy. Sift in the cake flour and baking powder and whisk just until combined. Do not overmix.
Beat the chilled egg whites on low speed until foamy. Gradually add the sugar and continue beating until the meringue is glossy and forms stiff peaks.
Add about one-third of the meringue to the egg yolk batter and gently whisk until combined. Fold in the remaining meringue in two additions, using a gentle bottom-to-top motion to preserve as much air as possible.
Preheat a large nonstick skillet over low heat, around 300°F (150°C). Lightly brush the surface with oil, then wipe away the excess so only a thin coating remains.
Scoop the batter into three tall mounds in the skillet, leaving space between them. Stack a second scoop of batter onto each mound to build their height.
Add 1 tablespoon of water to the empty spaces in the skillet, avoiding the pancakes. Cover immediately and cook for about 6–7 minutes over low heat.
Remove the lid and add another small scoop of batter to each pancake. Cover again and cook for another 2 minutes, allowing the pancakes to become taller and more stable.
Carefully flip each pancake using a spatula and a gentle rolling motion. Add the remaining tablespoon of water to the pan, cover, and cook for another 4–5 minutes, until the pancakes are golden on the bottom and cooked through.
While the pancakes cook, beat the heavy cream and sugar until medium-firm peaks form. Keep the whipped cream chilled until ready to serve.
Transfer the pancakes to serving plates immediately. Dust with confectioners' sugar and serve with whipped cream, fresh berries, and maple syrup.