Preheat the oven to 350ºF (180ºC). Line a baking sheet with parchment paper.
Mix the flour, oats, baking powder, and salt in a medium-sized bowl. Set aside.
Place the butter in the bowl of a stand mixer and mix it with the whisk attachment, on medium-high speed, until light and fluffy, about 3 to 4 minutes.
Add the brown sugar and continue to mix until smooth, about 2 minutes more, scraping down the sides of the bowl halfway through mixing.
Switch to the paddle attachment. Add the flour mixture to the mixing bowl. Mix on low speed until the dough starts to clump together and most of the dry bits at the bottom of the bowl are mixed in.
Dump the dough onto a lightly floured work surface and shape it into a smooth disc with your hands. With a rolling pin, roll the dough into a rough rectangle shape approximately 5x11-inches (28 x 13-cm) in size, and about ¼-inch (½-cm) thick.
Use a sharp knife to cut the dough into 12 even pieces. Using a small spatula, or an offset spatula, lift each oatcake onto the prepared baking sheet.
Place the oatcakes in the oven and bake them for 13 to 15 minutes, or until the edges are golden. Set the pan on a cooling rack and let the oatcakes cool completely. They will crisp up as they cool. Serve with tea, butter, cheese, fruit, or anything else you like.