Preheat oven to 325°F (170°C). Spray a 9-inch square baking pan with baking spray with flour. Line pan with parchment paper, letting excess extend over sides of pan.
For bars: In the bowl of a stand mixer fitted with the paddle attachment, beat butter, brown sugar, granulated sugar, and molasses at medium speed until light and fluffy, 2 to 3 minutes, stopping to scrape bottom and sides of bowl. Add eggs, one at a time, beating until combined after each addition and stopping to scrape sides of bowl. Beat in vanilla.
In a large bowl, whisk together flour, oats, salt, baking soda, baking powder, and cinnamon. With mixer on low speed, gradually add flour mixture to butter mixture, beating until just combined. Spread into prepared pan.
Bake until edges are golden brown and a wooden pick inserted in center comes out clean, 50 to 55 minutes. Let cool in pan for 10 minutes. Using excess parchment as handles, remove from pan, and let cool completely on a wire rack.
For icing: In a small bowl, whisk together confectioners’ sugar, 2 tablespoons (30 grams) water, salt, and vanilla until smooth. Pour and spread on cooled bar. Cut into pieces. Store in an airtight container for up to 3 days.