Prep an 8x8 inch pan by lining with parchment and preheat the oven to 350 degrees Fahrenheit.
In a medium, light-colored pan, melt butter over medium heat. Stir constantly as it begins to sputter/splatter. It will begin to smell nutty and small specks of brown will start to develop. DO NOT WALK AWAY FROM THE PAN AT ANY POINT. Once a decent amount of the specks are golden brown and it smells nutty, remove from the heat immediately and transfer right away to a heat-proof bowl to stop the cooking.
In a separate medium sized bowl combine cooled brown butter, brown sugar, white sugar, shredded zucchini and vanilla extract and whisk thoroughly. Add in oat flour, 2 cups of quick oats and salt, stirring till fully combined.
Pour into the 8x8 baking pan and press the top to smooth out the bars and get them compact. Bake at 350F for 25 minutes.
Allow the bars to cool completely before frosting and cutting. If they're not quite set, pop them in the fridge or freezer for about 20 minutes to cool further, which should help them come together.
Cream Cheese Frosting Drizzle
In a small bowl add milk and icing sugar to the softened cream cheese and whisk together thoroughly until smooth consistency. Drizzle over the bars using a fork (if you prefer thinner consistency) or transfer the icing to a piping bag and cut a very small hole in the tip and pipe over the bars (for a thicker consistency). Store in the fridge till ready to serve!
Notes
If making your own oat flour - pour rolled oats into a food processor and blend till you get a very fine, powdery flour. If you leave it a little more chunky, the bars won't hold together as well.
If you use regular rolled oats instead of quick oats, this recipe will still work, but will be a lot more chewy in texture and may not hold together as well.
Do not use "steel cut oats".
Brown butter burns very quickly! Having a bowl to transfer to quickly helps you immediately pull it off the heat and slow the cooking. Always pull it off a little before you think it's ready. The smell will be more nutty/toasted when it's ready!
If your bars aren't holding together well, the mixture may still be too warm or the flour was a little more chunky. It's ok! Just pop it into the freezer for 20-30 minutes. This should help it firm up. Keep the bars chilled in the fridge or freezer till ready to serve. Leave at room temperature for about 10 minutes before cutting into bars.