Preheat the oven to 350℉ and a line an 8x8 baking pan with parchment paper and set aside.
For the Brown Butter
Melt butter in a medium sauce pan on medium heat. Stir the butter to make sure it melts evenly. Once the butter is completely melted, it will start to foam up. Continue stirring the butter. As it cooks, it will start to change into a deeper color. This could take 6-8 minutes.You'll start to notice a nutty aroma and the butter will begin to have brown specs at the bottom of the pan. The entire process of browning butter from start to finish should not take more than 10 minutes on medium heat.
Once butter is browned, pour it into a heat proof bowl and set it aside to cool for about 5 or 10 minutes.
Caramel Oatmeal Bars
Wet Ingredients: In a medium bowl, add (slightly cooled) brown butter and brown sugar and mix using a spatula. Add the egg and vanilla extract and mix.
Dry Ingredients: Add the flour, quick oats, salt, and baking powder and mix, then add 1.5 oz of the chocolate (or chocolate chips if that's what you're using) and mix.
Spread in pan: Place ⅔ of the dough into the bottom of an 8x8 pan and spread it out completely.
First bake: Bake for 10 minutes, then remove it from the oven and sprinkle the rest of the chocolate on top. Then pour the caramel on top. (if it's not very pourable consistency, microwave it for about 20 seconds). If you need to, you can use a spoon or offset spatula and spread the caramel all over the chocolate. If it mixes together, that's fine.
Add remaining dough: Take the remaining dough and add it to the top of the caramel. Just flatten each piece a little with your fingers and place them all around. It won't cover the entire pan, but that's ok.
Second bake: Place back in the oven for 18-23 minutes until the edges are golden brown and you start to see the caramel bubble.
Cool: Remove from the oven and cool for at least 2 hours before slicing and enjoying.