Grease a 9-inch by 13-inch baking dish or line it with parchment paper.
In a saucepan over medium-low heat, melt the butter. Continue whisking the butter as it gently simmers until the butter is golden and you start to see flecks of brown at the bottom of the pan, after about 10 minutes. Transfer the butter to a large mixing bowl to cool for 30 minutes at room temperature, then another 30 minutes in the fridge, until it solidifies into softened butter.
Once the butter has solidified but is still soft, add the granulated sugar and mix with a large wooden spoon or silicone spatula until it’s light and creamy.
Add the peanut butter, vanilla extract and salt, and mix until it’s well combined.
Add the flour and cornstarch and gently mix just until it forms a dry, crumbly mixture. It should be able to hold its shape when you squeeze some in the palm of your hand.
Dump the dough into your prepared baking dish. Press the dough firmly in an even layer with the palm of your hand or the bottom of a drinking glass. Cover the baking dish with plastic wrap and refrigerate for at least 1 hour (or up to 3 days).
Preheat the oven to 350°F.
Bake the cookies for 18 to 22 minutes, until the edges just barely start to turn golden. Cool for about minutes, then slice into 16 even rectangles while it’s still slightly warm. Allow the cookies to cool for another 15 to 30 minutes in the baking dish, until they firm up a bit more to avoid breaking them.
Optional: Melt the chocolate and coconut oil in the microwave on 20 second intervals or on the stove, mixing to combine. Dip half of each rectangle cookie in the melted chocolate, then place it on a sheet of parchment paper. Sprinkle with flaky salt, and allow the chocolate to harden for about 20 minutes. Enjoy!!