Thaw the phyllo dough following the thawing instructions on the package.
Preheat the oven to 350 degrees F. Grease a 9-inch tart pan with a removable bottom.
Carefully unroll the phyllo dough and immediately cover it with plastic wrap. Overlay this with a slightly damp towel to ensure the dough does not dry out.
Using a pastry brush, lightly coat a single sheet of phyllo dough with the melted butter. Place the buttered sheet of phyllo dough onto the tart pan. Gently press the dough into the pan, making sure to cover the bottom and sides evenly.
Butter an additional sheet of phyllo dough. Place this sheet over the first, slightly offsetting it to ensure thorough coverage of the pan's surface. Continue this procedure with the remaining sheets of phyllo dough, applying a light coat of melted butter between each layer.
Fold and tuck the edges of the dough to create a ruffled look. Place a piece of parchment paper on the crust. Fill with pie weights or dried beans and bake for 20 minutes until golden brown and the crust is fully baked. Set aside to cool completely before filling.
When the crust is cool, increase the oven temperature to 375 degrees F.
Fill a saucepan with about 1 1/2 inches of water to make a double boiler and bring it to a simmer over medium heat. Combine the lemon juice and zest, sugar, butter, eggs, yolks, and salt in a large heatproof bowl.
Place the bowl onto the double boiler and whisk constantly, about 8 minutes, until the mixture thickens. Remove from the heat and whisk in the heavy cream.
Strain the lemon mixture through a fine mesh strainer. Pour the filling into the crust. Bake until the center is just set and slightly jiggly, about 12 – 15 minutes.
Remove the tart from the oven and place it on a cooling rack. Cool completely at room temperature, then chill in the refrigerator uncovered 2 hours or overnight.
Remove the tart from the pan using the removable bottom. Decorate with the blackberries and chocolate Robin Eggs.