Preheat your oven to 350°F. Line an 8-inch x 8-inch square pan with aluminum foil (either nonstick, or grease regular foil with cooking oil spray), and set it aside.
In a small saucepan, place the chopped butter and granulated sugar. Place over medium heat, whisking occasionally, until the butter melts and the mixture is gently simmering around the edges. Remove the mixture from the heat and set it aside to cool until it’s no longer hot to the touch.
In a large mixing bowl, place the eggs and vanilla, and beat with a handheld mixer until the mixture is a bit foamy.
Once the butter and sugar mixture is no longer hot to the touch, add it to the egg mixture and beat with the handheld mixer on medium speed until very smooth and well combined.
Add the cocoa powder to the mixing bowl and, with the mixer off, manually whisk the cocoa powder in just until the wet ingredients have absorbed the powder. Cocoa powder resists combining, so if you turn on the mixer right away, the powder will scatter.
Turn on the mixer to medium-high speed and beat until the batter very well-combined. It should be thick and glossy.
Add the oat flour and salt, and mix using a mixing spoon or spatula until just combined. Do not overmix.
Add about 4 of the 5 ounces of the chocolate chips, and mix until the chips are evenly distributed throughout the brownie batter.
The batter will be very sticky and thick. Scrape it into the prepared pan and smooth gently into an even layer with a slightly wet offset or silicone spatula.
Sprinkle the remaining chocolate chips evenly across the top of the batter, and press gently with your fingers to help the chips adhere to the batter.
Place the pan in the center of the preheated oven and bake for 20 minutes.
Reduce the oven temperature to 325°F and continue to bake for another 5 to 10 minutes, or until the brownies appear set all the way to the center. The brownies should not jiggle when you shake the pan gently from side to side.
The toothpick test is not useful here, so you’ll have to judge doneness based on appearance.
Remove the pan from the oven and allow the brownies to cool in the pan for about 1 hour or until the pan is no longer hot to the touch. The brownies will sink a bit as they cool, but they should sink evenly across the whole top.
Place the pan in the refrigerator to chill for about 1 hour or until very firm. Remove from the pan, slice with a sharp knife into 9 equal pieces and serve.