Heat oven to 350 degrees. Grease and flour a 10x15 jelly roll pan.
Add flour, salt and baking soda and mix on medium speed just until combined (about 1 minute). Pour into prepared pan and bake 18 to 22 minutes or until golden brown and a toothpick inserted in the middle comes out clean. Cool until just slightly warm and frost with Browned Butter Frosting (recipe below).
In a small saucepan, brown butter over medium heat until golden brown in color and golden brown flecks appear, swirling pan frequently. (Butter will become a little foamy). Remove from heat and pour into a medium size bowl, cool slightly. Add powdered sugar, vanilla and half & half, mix until smooth and spreadable. (I like to use my hand mixer for this).