Whisk together the egg, milk, and salt in a bowl until well combined. Add the flour, baking powder, and icing sugar, stirring until you have a smooth batter with no lumps. The batter should be thin enough to spread easily in a skillet. Transfer to the refrigerator and chill for 45-60 minutes—this resting time allows the flour to fully hydrate and helps the crepes cook more evenly and become slightly more tender.
While the batter chills, combine the softened cream cheese, icing sugar, milk, and vanilla in a bowl. Beat until smooth and spreadable, making sure there are no lumps of cream cheese. The filling should be creamy but hold its shape when spread on the crepes. Set aside at room temperature until ready to use.
In a small saucepan over medium heat, combine the fresh raspberries with the fresh lemon zest. Cook, stirring occasionally, for 5-8 minutes until the raspberries break down and the mixture becomes thick and syrupy. The berries will release their natural juices and concentrate as they cook. This sauce should be made while the batter is still chilling so it has time to cool slightly before assembly.
Heat a nonstick skillet or crepe pan over medium-low heat and add 1 tbsp of melted butter, swirling to coat. Once the skillet is hot, pour about 1/4 cup of chilled batter into the center and immediately tilt and rotate the skillet to spread the batter into a thin, even layer—working quickly is key here. Cook for 30-45 seconds until the bottom is light golden brown, then flip and cook the other side for about 30 seconds. Transfer the cooked crepe to a plate and repeat with the remaining batter. I find that medium-low heat prevents the crepes from browning too quickly on the outside before cooking through.
Place a cooked crepe on a serving plate and spread about 1 tablespoon of the cream cheese filling from Step 2 onto the surface. Spoon some of the cooled raspberry sauce from Step 3 over the filling, then roll or fold the crepe. Top with a dollop of whipped cream and garnish with fresh raspberries if desired. Serve immediately while the crepes are still warm and the filling is at its best texture.