Preheat the oven to 350 degrees F. Spray a 9-inch cake pan with nonstick baking spray and dust with flour. Line the pan with parchment paper and spray again.
Combine the brown sugar and 1 stick of butter in a small saucepan. Cook over medium-low heat, stirring frequently, until the butter melts. Pour the mixture into the prepared cake pan. Top with the walnuts.
Beat the granulated sugar and remaining 1 stick butter in a large bowl at medium speed with a mixer until fluffy. Beat in the vanilla. Add the egg yolks, beating until combined.
Combine the flour, baking powder and salt in a medium bowl. Gradually add the flour mixture to the butter mixture alternately with the milk, beginning and ending with the flour mixture, beating just until combined after each addition.
Beat the egg whites in a separate bowl until stiff peaks form. Gently fold the egg whites into the batter. Add the cranberries and spoon over the mixture in the prepared pan.
Bake until a wooden pick inserted in center comes out clean, 35 to 40 minutes. Cool the cake in the pan, about 10 minutes. Immediately invert the cake onto a serving platter. Cool before serving, about 15 minutes.