Preheat the oven to 325 degrees.
Line 2-3 baking sheets with parchment paper or silicone baking mats.
Combine the softened butter, peanut butter, light brown sugar, white sugar, vanilla extract, 1 egg, and 1 egg yolk in the bowl of a stand mixer (or a mixing bowl you can use with a handheld electric mixer). Beat on medium-high until it has lightened in color and is fluffy and airy, this should take about 4-5 minutes.
While the mixer is off, pour in the flour, salt, baking powder, and baking soda. Mix on low until just combined. Add the peanut butter chips and give one last good mix.
Scoop mounds of the dough using a spoon or cookie scoop onto your parchment-lined baking sheets. The cookies won’t spread too much but it is a good idea to leave approx 2” in between each cookie.
Place the cookies in the preheated oven, and bake for 6 minutes. Take the cookies out of the oven, working quickly but carefully, drop the tray of cookies onto your counter from about 5” up, or firmly hit the bottom of the cookie tray onto your counter. Repeat this action 4-5 times, this will help the cookies to spread out into a cookie shape, you will repeat this process one more time after the cookies are done baking. Return the cookies to the oven for an additional 3-4 minutes. The cookies should still be light in color when you take them out.
Remove the cookies from the oven when they have finished baking, repeat the process of carefully and firmly dropping the cookie tray onto the countertop another 3-4 times, then let the cookies cool on the tray.
Once the cookies have cooled, place the dark chocolate chips into a microwave-safe dish. Heat in 15-second intervals, stirring in between until melted.
Dip each cookie about halfway into the melted chocolate. Immediately sprinkle with a tiny bit of flake finishing salt. Let the chocolate cool and dry completely.
These cookies are best served the same day or the next day but can be stored in an airtight container for up to 5 days.