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

In a large mixing bowl, cream the softened butter with both granulated and brown sugars on medium speed until fluffy, about 3 minutes.

Beat in the eggs one at a time, then mix in the vanilla extract until fully combined.

Whisk together the flour, baking powder, and salt in a separate bowl. Gradually add the dry ingredients to the wet ingredients until just combined.

Press the majority of the dough evenly into the prepared pan, creating a smooth base.

Mix the melted butter, brown sugar, cinnamon, and cardamom in a separate bowl until well combined. Spread the filling over the base layer.

Dollop the reserved dough over the filling and swirl gently with a knife or toothpick to create a marbled effect.

Bake for 28 to 32 minutes until the edges are golden brown and the center is slightly soft. Let cool completely on a wire rack.

Beat cream cheese and softened butter until smooth. Gradually add powdered sugar and vanilla. Adjust consistency with heavy cream if needed.

Spread the frosting evenly over the completely cooled bars and slice into squares for serving.