Preheat oven to 375° Roll out pie dough into a 12-inch circle on a surface liberally sprinkled with flour. Fit into a standard 9-inch pie pan and flute the edges. Prick the bottom of the dough with a fork.
Line with a piece of parchment paper and fill with dried beans, uncooked rice, or pie weights. Bake for 20 minutes. Remove the paper with pie weights and bake for an additional 15 minutes (or until crust is starting to get golden brown.) Let the crust cool on a wire rack while you make the filling.
Reduce the oven temperature to 350°. Make the blackberry filling: In a medium sauce pan mix together sugar and cornstarch. Add blackberries and lemon juice and cook over medium-high heat, stirring and breaking up the blackberries as much as possible with a wooden spoon or potato masher, until the filling has thickened and the berries have fallen apart, 3 to 5 minutes. Remove from heat and let cool.
Make the Chess Pie Filling: Combine the sugar and cornstarch. Whisk in butter, cream, eggs, egg yolks cornmeal, lemon juice and zest, and vanilla in a large sauce pan. Cook over medium heat, stirring constantly with the whisk, until the filling has thickened a bit and coats the back of the spoon, about 7 minutes. It should be the consistency of thin lemon pudding. Remove from heat.
Assemble the pie by spooning most of the blackberry filling into the bottom of the baked pie crust. Reserve 2 tablespoons of the blackberry filling for the top. Gently pour or spoon the lemon chess filling over the blackberry filling, trying to disturb the blackberry filling as little as possible. Don’t overfill the pie. Spoon the remaining blackberry filling on top and decoratively swirl the blackberry filling with the lemon filling.
Bake until the edges of the pie filling start to brown, 35 to 45 minutes. Let cool to room temperature before serving.