Blend the gluten free flour, eggs, milk, melted butter, granulated sugar, salt, and vanilla in a blender until completely smooth. Let the batter rest in the refrigerator for at least 30 minutes. This rest is essential for tender, pliable crepes.
Heat a 9 or 10-inch nonstick skillet over medium-low heat and lightly grease with butter. Pour about 3 tablespoons of batter into the pan, swirling quickly to coat the bottom in a thin, even layer. Cook for about 60 seconds until the edges lift, then gently flip and cook for another 20 seconds.
Repeat with remaining batter to make 18 to 20 crepes. Stack them on a plate with a small piece of parchment between each. Let cool completely.
Whip the heavy cream and powdered sugar together until medium-stiff peaks form. Gently fold in the softened mascarpone and vanilla until smooth and combined. Be careful not to overmix or it can become grainy.
Place one crepe on your serving plate. Spread a thin, even layer of the mascarpone cream over the top, about 2 to 3 tablespoons. Arrange a single layer of sliced strawberries over the cream.
Top with another crepe and repeat the layering process, alternating between cream-only layers and cream-with-strawberry layers. Continue stacking all the crepes, finishing with a plain crepe on top.
Cover the cake gently with plastic wrap and refrigerate for at least 4 hours, or overnight. This resting time allows the layers to meld and makes the cake slice beautifully.
When ready to serve, dust the top generously with powdered sugar and arrange a few fresh strawberry slices on top. Slice with a sharp motion straight down for the cleanest layers.