Step 1: In a large bowl, whisk together the eggs, granulated sugar, and salt. Slowly add the milk and vanilla extract, whisking until combined.
Step 2: Gradually sift the cake flour into the wet mixture, whisking constantly to prevent lumps. Stir in the melted butter.
Step 3: Strain the batter through a fine-mesh sieve into a clean bowl to ensure it is perfectly smooth. Cover and refrigerate for at least 1 hour.
Step 4: Heat a 10-inch non-stick skillet over medium-low heat. Lightly brush with butter. Pour about 1/4 cup of batter into the pan, swirling quickly to coat the bottom thinly.
Step 5: Cook for about 60-90 seconds until the edges are dry and slightly golden. Carefully flip and cook the other side for 15 seconds. Remove to a wire rack to cool. Repeat until all batter is used (aiming for 20-25 crepes).
Step 6: In a cold bowl, whip the heavy cream and powdered sugar until stiff peaks form. Be careful not to over-whip into butter.
Step 7: Place the first cooled crepe on a serving plate. Spread a thin layer of whipped cream (about 3 tablespoons) evenly to the edges.
Step 8: Every 4 layers, place a single layer of very thinly sliced mangoes on top of the cream, then top with another crepe.
Step 9: Repeat the process until all crepes are used, ending with a plain crepe or a thin layer of cream topped with decorative mango slices.
Step 10: Chill the finished cake in the refrigerator for at least 4 hours (or overnight) to allow the layers to set before slicing.