Italian Lemon Cream Cake

Ingredients:

For the cake:

1 cup all-purpose flour
1 cup granulated sugar
1/4 cup unsalted butter, softened
1/2 cup whole milk
1 1/2 teaspoons baking powder
1/2 teaspoon salt
4 large eggs
1 tablespoon lemon zest
2 tablespoons lemon juice

For the lemon cream filling:

1 cup heavy cream
8 ounces cream cheese, softened
1 cup powdered sugar
2 tablespoons lemon juice
1 tablespoon lemon zest

For the frosting:

1/2 cup unsalted butter, softened
2 cups powdered sugar
1 teaspoon vanilla extract
1 tablespoon heavy cream (more if needed)