When making the pastry cream, instead of using 1 cup heavy cream and 1 cup milk, you can use 2 cups of half and half. I don't recommend freezing this cake because the pastry cream can break. To make the ganache shiny for longer, you can add 1-2 tablespoons of light corn syrup if you have it, heating it along with the cream.
In a small saucepan or in the microwave, heat butter and milk just until butter is melted. Do not let it boil. Set aside.
In a mixer bowl fitted with the whisk attachment, whisk eggs and sugar on high speed for 5 minutes. Beat in vanilla extract. Reduce speed to medium-low and add warm milk-butter mixture into the egg mixture in a slow, steady stream. Add flour mixture in 3 additions and fold by hand using a rubber spatula just until combined.
Pour batter into prepared cake pans and smooth the top. Bake for 20-25 minutes, until the cake springs back when slightly touched and a skewer inserted into the center comes out clean. Allow cakes to cool on a wire rack for 20 minutes, then run a knife around the edges and invert the pan onto the rack. Let cool completely. Refrigerate cakes for at least 1 hour before assembly to ensure the interiors are completely cooled and not too soft.
In a medium saucepan, heat heavy cream and milk on medium heat just to a boil. Remove from heat and gradually pour the hot milk into the egg mixture while simultaneously whisking constantly until smooth (this will prevent the eggs from being cooked by the heat). Transfer mixture back into saucepan. Cook over medium-low heat, whisking constantly and vigorously so that the eggs won’t curdle, until mixture thickens and bubbles burst on the surface. Remove from heat and whisk in vanilla and butter. Strain through a fine-mesh strainer set over a bowl. Press a piece of plastic wrap directly onto the surface of the cream to prevent it from creating a skin. Let cool to room temperature, then refrigerate until chilled.
Assembly: Place one cake layer on a plate or cake stand. Spread pastry cream evenly on top. Place second cake layer on top and gently press down to adhere to the pastry cream. Pour glaze into the center of cake, then gently spread it to the edges, allowing it to drip down the sides.
Keep cake in the fridge, covered, for up to 4-5 days. Allow it to come to room temperature before serving. I don't recommend freezing the cake because the pastry cream can break if frozen.