In the bowl of a stand mixer combine the softened unsalted butter, brown sugar and white sugar. Cream together with a paddle attachment until the butter and sugars are well mixed. Scrape down the sides of the bowl and then turn the mixer on high. Beat on high for 2 minutes.
Add the peanut butter to the mixer and mix on low to combine the ingredients. Scrape down the sides of the bowl and then turn the mixer on high. Beat on high for 2 minutes.
Add the eggs and vanilla extract to the mixer and cream together with the peanut butter mixture. Scrape down the sides of the bowl and bottom of the bowl. Turn the mixer on high and beat for 2 minutes. Scrape down the sides of the bowl and check that the mixture is completely emulsified and there are no streaks of butter that haven't been fully incorporated.
Meanwhile combine the flour, baking powder, baking soda, and kosher salt in a bowl and whisk together. When the wet ingredients have been fully mixed add the dry ingredients all at once to the mixer. Turn on the mixer to low and mix for 20 to 30 seconds or just until it as all combined.
When the dough is finished it needs to chill for at least 1 hour. Either transfer the dough to a covered bowl and refrigerate for 1 hour or portion the dough onto a parchment lined baking sheet. I like to use a 2 oz scoop to portion the dough onto a small baking sheet. The dough can be portioned close together to fit it onto one tray and then divided between more baking sheets before baking. Cover the dough with cling film while chilling.
While the dough is chilling preheat the oven to 350°F / 177°C. Transfer the portioned dough onto parchment lined baking sheets making sure to leave 2 inches between them to allow for spread.
Bake for 13 to 15 mintues or until the edges are very lightly turning brown and the tops give a slight resistance when touched. Remove the trays from the oven. Let the cookies cool on the tray for a couple of minutes before sliding the parchment and cookies off onto a wire rack or the counter to cool completely. Store in an air tight container at room temperature.