Preheat the oven to 350°F (175°C) and line a 9x13 inch baking pan with parchment paper.

In a mixing bowl, combine softened unsalted butter, granulated sugar, and brown sugar. Beat until light and fluffy, about 3 minutes.

Gradually add the eggs one at a time, mixing in vanilla extract until combined.

In a separate bowl, whisk together all-purpose flour, baking powder, and salt. Gradually add to wet ingredients, stirring until just combined.

Set aside 1 cup of dough. Press remaining dough into the bottom of the prepared baking pan.

In another bowl, mix melted butter, brown sugar, cinnamon, and cardamom until smooth. Spread over the pressed dough.

Drop spoonfuls of reserved dough over the cinnamon filling and swirl with a knife or toothpick.

Bake in the preheated oven for 28 to 32 minutes, until edges are golden while the center is slightly soft.

Allow to cool completely in the pan on a wire rack.

For frosting, beat cream cheese and butter until smooth. Gradually add powdered sugar and milk until desired consistency.

Spread frosting over cooled bars, then slice into squares.