To make these cookies, start by preheating your oven to 350 F.
While the oven is preheating, brown the butter. Add the salted butter to a small or medium-sized saucepan, on the stove, over medium heat, swirling the pan occasionally until the butter starts to brown and smell nutty. This will take approximately 3-5 minutes.
As soon as the butter starts to foam and turn brown, remove it from the heat - this is very important, to ensure that the butter doesn't burn.
Next, add the browned butter to the bowl of a stand mixer, alongside the coconut sugar and monk fruit sweetener or organic cane sugar, and mix until they're fully creamed and combined.
Then, add in the whole egg, egg white, and the vanilla extract, and mix until just combined.
Once the wet ingredients have fully combined, add in the dry ingredients: the flour, baking soda, sea salt, and oats. Chop the peanut butter cups and add them to the bowl, then mix until just combined and a cookie dough has formed.
Line a baking sheet with parchment paper, then use a cookie scoop to scoop the dough into balls, lining them up on the baking sheet approximately 2 inches apart. If using a large cookie scoop, you should end up with 12 cookies. If using a smaller cookie scoop, you should end up with closer to 16 cookies.
Transfer the cookies to the oven and bake them for 8-10 minutes. If you prefer a softer cookie, stick to 8-9 minutes; if you prefer a crispier, more well-done cookie, 9-10 minutes is perfect.
Once the cookies are done, remove them from the oven and garnish them with a sprinkle of flaky sea salt (if desired).
Allow the cookies to cool completely, then serve and enjoy! Store any leftovers in an airtight container, in the fridge, for up to one week.