Preheat the oven to 350°F (180°C) and line a 9-inch (22 cm) cake pan with parchment paper.
In a large bowl, whisk together the flour and baking powder.
In another bowl, cream together the butter and sugar until light and fluffy. Add the eggs one at a time, beating well after each addition.
Stir in the vanilla extract and milk. Gradually fold in the dry ingredients until just combined.
Pour the batter into the prepared pan and bake for 30-35 minutes, or until a toothpick inserted into the center comes out clean.
Let the cake cool completely, then slice it horizontally into two layers.
Prepare the vanilla cream: cook the vanilla pudding according to the package instructions, then let it cool completely.
Whip the heavy cream to stiff peaks, then gently fold in the cooled pudding and powdered sugar.
Spread the vanilla cream over the bottom cake layer, then top with the second layer and frost the entire cake with the remaining cream.
Garnish the cake with whipped cream or fresh fruit, and refrigerate for at least 1 hour before serving.
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