Whisk eggs with sugar, butter and vanilla in a medium mixing bowl. Stir in half of the milk until the mixture is smooth.
Add the flour and sprinkle baking powder and salt on top. Whisk by hand (or beat on low speed with a mixer) until the batter is smooth and lump-free.
Lastly, add the rest of the milk and mix until smooth. Allow the batter to sit at room temperature for about 15 minutes (this allows the thickener in the flour to thicken the batter, which is what makes thick, fluffy pancakes).
Heat a non stick pan (or a cast iron pan) over medium heat. Add a teaspoon or so of neutral-tasting oil (like sunflower oil) or butter. For each pancake, ladle about 1/4 cup (60 ml) of batter into the hot pan.
Cook for about 2-3 minutes, until you see bubbles forming in the batter and the edges of the pancake begin to look less wet (they go from looking glossy wet to a waxy dry-ish sheen). Flip the pancake and cook for another 60 seconds or until the other side is golden brown too. Continue with the rest of the batter and add more oil or butter to the pan as needed (usually after every second pancake). Transfer pancakes to serving plates. Top with a dollop of mascarpone cheese, sliced berries, a sprinkle of powdered sugar and plenty of maple syrup.