Preheat oven to 350°F. Line an 8x8 inch baking pan with parchment paper. Set aside.
Melt butter and transfer to a medium size bowl. Set aside to cool. Meanwhile, pulse oats in a food processor. Do not pulse so much that the oats become flour.
In separate bowl, whisk together pulsed oats, flour, baking soda, cinnamon and salt. Set aside.
To the bowl with the melted butter, add sugar and brown sugar. Mix on low for one minute. Mixture will resemble wet sand.
Add the egg, then the vanilla and molasses. Mix to combine well.
Add the dry ingredients to the butter and sugar mixture. Use a large spatula or to fold the mixture together just until the flour is incorporated. Do not over mix.
Transfer dough to prepared baking pan. Bake for 20 to 24 minutes or until the edges are set and the top is golden brown. Do not over bake or the cookie bars will be dry.
Remove the bars from the oven and cool in the pan on a wire cooling rack. Be sure the bars are cool to the touch before adding the icing.