1. Preheat the oven to 350°F. Line an 8 × 8-inch baking pan with parchment paper and set aside.
2. Melt the butter and transfer it to a medium bowl. Let it cool for about 10 minutes. Meanwhile, pulse the oats in a food processor until cut into smaller pieces. Do not process them into oat flour.
3. In a separate bowl, whisk together the pulsed oats, flour, baking soda, cinnamon, and salt. Set aside.
4. Add the granulated sugar and brown sugar to the melted butter. Mix on low speed or whisk for 1 minute, until the mixture resembles wet sand.
5. Add the egg, followed by the vanilla and molasses. Mix until well combined.
6. Add the dry ingredients to the butter mixture. Fold with a large spatula or wooden spoon just until the flour is incorporated. Do not overmix.
7. Transfer the dough to the prepared baking pan. Bake for 20–24 minutes, or until the edges are set and the top is rich golden brown. Do not overbake.
8. Remove the pan from the oven and let the bars cool on a wire rack for 1–2 hours, until they reach room temperature. Make sure they are cool to the touch before icing.

Vanilla Icing

1. In a medium bowl, whisk together the powdered sugar, 1 tablespoon of milk, and vanilla until thick but smooth. Add more milk as needed. If the icing is too thin, add powdered sugar one tablespoon at a time.
2. Once the bars are completely cool, use a spoon to spread the icing over the tops, leaving small areas of the cookie bars visible.
3. Allow the icing to set, then slice into squares and serve.