In a medium-size mixing bowl, sift 2 cups of flour, then add the salt, grated lemon zest and sugar. Whisk the dry ingredients together. Add egg yolks, egg, vanilla, rum, and butter flavor extract. [Note: if preferred, substitute rum flavoring for the rum.] Stir the ingredients with a wooden spoon to mix. Add the softened butter, in 2-tablespoon portions (approximately), and mix into the dough, first with the wooden spoon and then by hand. If the dough is too sticky, add flour (about 1 tablespoon at a time) and hand mix. Dough should be smooth and nonsticky, and with the consistency resembling a very soft pie dough.

Cover the bowl with plastic wrap or a plastic lid. Allow the dough to rest at room temperature for about an hour. After the rest, place the dough in the refrigerator for an additional hour, or overnight.

In a blender, add the cream, the flour, cornstarch, salt, and sugar. Blend to thoroughly mix the flour and cornstarch into the liquid, with no lumps.

Using a stainless steel mixing bowl and a large pot that can fit just under the mixing bowl, make a bain-marie setup. Add about 1 - 2 inches of water to the pot. Place the mixing bowl on top of the pot, such that the rim of the pot supports the mixing bowl. Pour the liquid from the blender into the mixing bowl. Turn on the heat beneath the pot and gently bring the water to boil, while whisking the liquid ingredients in the mixing bowl. Add the egg yolks, white chocolate and the butter flavoring to the cream liquid mixture, while continually whisking the bowl. Continue whisking the bowl as the bain-marie warms the contents of the mixing bowl. The cream and egg yolk mixture will form a pastry cream that has a thick pudding-like consistency. It is important to stir the mixture constantly, and not to allow the mixture to scorch. When the pastry cream has heated and reached a nice thick pudding-like consistency, remove from heat. Add the vanilla extract and rum to the pastry cream and whisk thoroughly. Cover the mixing bowl with plastic wrap or foil and put the pastry cream in the refrigerator to cool for at least 1 hour.

1. Preheat oven to 375 degrees Farhenheit (190 Celsius).

2. Remove the chilled dough from refrigerator and divide into to parts, one just a bit larger than the other. One portion will be used to form the bottom of the gateau and the second portion will form the top. Using two sheets of waxed paper, roll out the larger portion of dough into a circular shape about 1/4-inch thick (more or less) and about 1 inch larger than the diameter of the 8 - 9 inch cake pan (or pie pan). Carefully line the bottom and sides of the cake pan with the dough, bringing the dough to the top edge of the pan. It is important that the dough extend to the top of the pan.

3. Remove the chilled pastry cream mixture from the refrigerator and spoon into the dough-lined cake pan. Use a spatula to evenly spread the pastry cream inside the pan. Using a spoon, mix the cherry preserves in their jar. Spoon the cherry preserves onto the top of the pastry cream, being careful not to mix them into the pastry cream. The cherries are a top layer, not part of the pastry cream. When the cherry preserves are spread over the top of the pastry cream, sift the dark chocolate cocoa powder on top of the preserves.

4. Roll out the second portion of the dough into a circle that is just slightly larger than the top of the cake pan. Carefully place the rolled-out dough on top of the cake pan. Pinch the edges of the bottom and top layers of the dough together using a fork.

5. Using a knife, make a diagonal cut across the center, stopping about 1 inch from the outer rim of the cake pan. Next, make about 4-5 cuts at an angle to the first one, one each side of the diagonal cut, making a "basque" tree-like pattern.

6. Beat an egg, and brush it onto the top of the gateau to make a rich glaze.

Place the gateau basque on the lowest shelf of the oven, and bake at 375 degrees Fahrenheit (190 Celsius) for about 40 minutes. The crust will turn a rich golden brown, and the cuts will make an artistic pattern. The tree shape is a traditional Basque symbol.

Allow the baked gateau to cool completely. [At this stage, it is optional to pour about 1/4 cup of dark rum over the gateau, and let the rum be soaked up by the cake. You may need to pour the rum in small amounts, a couple of tablespoons at a time, to avoid spilling over the edge of the cake pan.] Place the gateau basque in the refrigerator to chill, preferably overnight.

Serve chilled or at room temperature; but, it is easiest to cut the gateau after the pastry cream-and-cherry filling is cool, to minimize oozing of the filling.