Heat the oven to 350℉. Line a 10 or 12-inch oven-safe skillet (I used a cast iron pan) with a circle of parchment paper.
In a large bowl, whisk together the ½ cup unsalted butter, ½ cup packed dark brown sugar, and ½ cup granulated sugar until creamy. Whisk in the 1 large egg and 1 tablespoon vanilla extract.
Stir and whisk in the 1 ¾ cups oat flour, ¾ teaspoon baking soda, and ½ teaspoon fine sea salt until just combined. Fold in the 1 cup semi-sweet chocolate chips.
Spread the batter evenly in the prepared skillet. Rest for 20 minutes to hydrate the flour, then bake until golden brown and set but still slightly soft in the center, about 25 minutes. Let stand for at least 5 minutes before serving warm or at room temperature.
Notes
Use a cast iron skillet. I love using my cast iron skillet (bought used at Cookin - RIP - in San Francisco over 20 years ago now) whenever possible (see my gluten free pumpkin cornbread for another nice way to make good use of the cast iron). It is sturdy and distributes heat wonderfully, ensuring even baking. That said, if you don't have a cast-iron skillet, any oven-safe skillet will work.
Try a gluten free flour mix. If you wish, use a 1:1 all-purpose gluten free flour blend (like my homemade gluten free flour blend) instead of the oat flour. Make sure to measure it by weight (210 grams) for accuracy.
Don't overbake. This is always a bit tricky with gluten-free recipes because they tend to take longer to bake than regular recipes, but - pull the skillet out of the oven even if the center doesn't look totally set. This helps the cookie achieve that lovely fudgy texture (you can also cook it a bit longer to make sure it sets if you don't like to err on the side of underbaking. It will still taste delicious.)
Then rest a bit. I love serving this cookie warm, and recommend doing so. However, try to let it rest for 15 minutes to fully set. It will still be warm and gooey.
Brown the butter. For extra depth of flavor, brown the butter first. Heat the butter in a pan set over medium heat, then cook for about 5-8 minutes until the butter is browned and smells nutty.