Preheat the oven to 350°F (175°C). Line an 8x8-inch square pan with enough parchment paper to have an overhang on all sides.

In a small bowl, mix the brown sugar and cinnamon for the filling until thoroughly combined. Set aside.

Whisk melted butter, white sugar, brown sugar, vanilla, salt, and nutmeg until thoroughly combined.

Add in egg and egg yolk and mix until thoroughly combined.

Add in flour and baking soda and mix until just incorporated.

Spread half the batter into an even layer in the prepared pan. Sprinkle the cinnamon-sugar mixture evenly over the batter.

Place dollops of the remaining batter over the cinnamon-sugar layer and carefully spread it into an even layer.

Bake in the preheated oven until bars puff up in the middle, are golden brown, and pull away slightly from the edges, about 25 to 30 minutes.

Allow the bars to cool completely in the pan.

For the glaze: Beat cream cheese, powdered sugar, vanilla, and salt together with an electric mixer until completely smooth.

Add heavy cream and beat until smooth, adjusting consistency with more cream or powdered sugar if necessary.