Preheat the oven to 325°F. Line a 9x9-inch pan with parchment paper and spray lightly with cooking spray.
In a medium mixing bowl, combine the flour, oats, both sugars, baking powder, baking soda, and salt. Stir with a whisk to combine.
Stir in the melted butter until combined.
Set aside 1 cup of the mixture to use for the topping. Press the remaining mixture into the bottom of the prepared pan.
Bake for 8 minutes until light golden brown. Set aside to cool while you make the filling.
Make the filling
In a small mixing bowl, combine the flour, sugar, and salt. Stir with a whisk to combine.
Place chocolate and butter in a large heat-proof bowl set over a pot of barely simmering water. Stir with a silicone spatula until chocolate has melted completely. Remove from heat.
Whisk in the eggs, one at a time. Stir in the flour mixture until combined. The mixture will resemble thick brownie batter.
Pour over the cooled crust. Sprinkle the top with the remaining oatmeal mixture.
Bake for 30 to 35 minutes, until the edges are set and have browned lightly. Cool in the pan on a wire rack for 1 hour.
Remove from pan and cut into squares. For neat slices, refrigerate for 2 hours before cutting.
Notes
Oats: quick-cooking oats are required. Old-fashioned rolled oats will leave the bars extra dense and chewy. If you don't have quick-cooking oats, you can pulse rolled oats in a food processor to break them down some.
Chocolate: Use bars of baking chocolate for best results. Chocolate chips don't melt as smoothly.
Make ahead tip
The bars will stay fresh in an airtight container in the refrigerator for up to 3 days.
The bars also freeze well. Cool them completely the slice and wrap them individually in plastic wrap. Place the wrapped bars in a sturdy container with an airtight lid and freeze them for up to 3 months.
Thaw them in the refrigerator overnight when you are ready to serve them. You can eat them cold or set them out to come to room temperature.