To make the filling: In the bowl of a stand mixer combine the eggs and the sugar and beat on high speed until the mixture triples in volume. Beat in the flour and 2 teaspoons vanilla. Meanwhile heat the butter over medium-high heat until it browns. Beat the brown butter into the batter, being sure to scrape all of the browned butter bits from the bottom of the pan. Let the batter rest for about 20 min.
To assemble the tart: Preheat oven to 400 degrees F.
Using a rolling pin, roll the puff pastry out until it is large enough to fill a 10-inch removable bottom tart mold. Line the tart mold with the dough then dock or poke the dough with a fork in several spots. Place parchment paper on top of the dough and fill with the beans. Bake for about 10 to 12 minutes. Remove from the oven and let cool. Add the lemon zest to the brown butter batter. When the crust has cooled add the fruit and pour the brown butter batter over the top. Return to the oven and bake for about 20 minutes. The top should be slightly souffled and the inside will be set but still moist. Allow to cool to room temperature. Mix the mascarpone cheese with 2 teaspoons of vanilla extract. Dollop a spoonful of vanilla mascarpone on each slice of tart before serving.