To make the browned butter: add 1 stick of the butter to a small saucepan over medium-low heat. Allow the butter to cook until medium brown in color and nutty smelling. The butter turns from brown to burned quickly, so keep an eye on it always and only cook over low heat. Remove from the heat and cool slightly.
Grease and line an 8x8 baking pan and line with parchment paper.
In the bowl of a stand mixer fitted with the paddle attachment, add the browned butter, remaining stick of butter, vanilla, cinnamon and brown sugar. Beat on medium speed until well combined, about 2 minutes. Add the eggs and beat for another minute.
In a separate bowl, whisk together the flour, salt and baking powder. Add the dry ingredients to the wet, along with the cranberries and white chocolate and mix until just combined.
Press the batter into the prepared pan and freeze for 15 minutes.
Preheat an oven to 350 degrees F and bake for 35-40 min, until golden brown on top. Cool completely to room temperature.
To make the frosting: in the bowl of a stand mixer fitted with the paddle attachment or a bowl using a hand mixer, beat the cream cheese and powdered sugar until smooth. Add the heavy cream and vanilla and beat until smooth. Add the melted white chocolate and beat for 1 minute, until completely combined.
Spread the frosting on the cooled bars and refrigerate for 30 min. Cut into triangles and top with more cranberries and drizzle melted white chocolate on top, if desired.