GET READY: Line a 9 by 13 pan with parchment paper, so that it extends over the sides along the long side, like handles. This makes it easier to remove the bars. In a medium bowl, stir together flour, salt and cardamom with a whisk until well incorporated. Adjust oven rack to the middle position and preheat oven to 275 degrees F.
MAKE DOUGH: Cream 1 cup of unsalted butter with the brown sugar and granulated sugar, until light and fluffy. Add egg yolk and beat until well blended, followed by vanilla extract, scraping sides of bowl with a rubber spatula as needed until well blended. Add flour mixture gradually on low speed until just combined.
SPREAD & BAKE DOUGH: Break dough into pieces and spread evenly into 9 X 13 pan, using a rubber spatula, offset spatula or a small piece of parchment paper and your hand. Beat reserved egg white and brush on top of dough. Sprinkle pecans over the egg white. Bake at 275 degrees for 50-55 minutes.
MAKE FROSTING: While the cookies bake, melt 1.5 tablespoons of butter over medium heat in a small saucepan, until it browns slightly, about 4-5 minutes. Remove from heat. Whisk in powdered sugar, vanilla, a pinch of salt, and enough milk make to make a “drizzly” consistency.
FROST & CUT COOKIES: Remove cookies from oven and cool slightly. Drizzle with icing, and cut into bars or triangles while they’re still warm. Allow to cool fully for frosting to set.