In a small saucepan over medium heat, melt 4 Tbsp butter. Once melted, add oats and stir for about 5-7 minutes, until browned and toasted. Pour oats onto a baking sheet lined with parchment paper.
In a medium bowl, whisk together flour, baking soda, and salt.
In the bowl of a stand mixer or in a large bowl with a hand mixer, beat together 1 stick butter, brown sugar, and granulated sugar until fluffy, about 2-3 minutes. Add peanut butter and continue mixing until well-combined.
Add the flour mixture to the bowl and mix until just combined, taking care not to over-mix. Gently fold in the oats.
Put the dough on a large sheet of parchment paper. Put another sheet of parchment paper over the top and roll the dough out with a rolling pin, until it’s about 1/4 inch thick and even. Place the dough onto the back of a cookie sheet and put in the fridge for 20-30 minutes.
Pre-heat oven to 350 degrees and line two baking sheets with parchment paper.
Place dough on the counter and take the top sheet of parchment paper off. Using a 2-inch round cookie cutter (or biscuit cutter), cut 24 cookies out of the dough.
Place cookies about 1 inch apart on prepared baking sheets. Bake for 9-11 minutes, rotating sheets halfway through, until cookies are just turning golden.
Let cookies cool in the pan for a couple minutes before moving to wire racks to cool completely.