First, add the peanuts to a dry, non-greased pan and roast, stirring occasionally to prevent burning, for 3 to 4 minutes, until they've darkened slightly. Transfer to a clean kitchen towel, and cover the peanuts with the towel and rub them with your hands to separate the peels. Slice or break the peanuts in half and transfer to a bowl to cool.
Now preheat the oven to 175 C. Line a baking tray (or two if you're baking in batches) with silicone baking mats. Set aside.
In a mixing bowl, beat the butter and sugars using a hand mixer, until pale and fluffy. Add the peanut butter and beat briefly to combine.
Add the egg and vanilla and beat again till combined.
Sift in the flour, baking soda, baking powder and salt, if using. Fold to combine into a thick, sticky dough. Lastly, fold in the chocolate chips and the chopped, roasted peanuts, dispersing them evenly through the dough.
Cover the bowl with clingfilm and chill it for 20 to 30 minutes, which makes it easier to scoop the sticky dough. If chilling for an hour or longer, the dough will need to sit at room temperature before you are able to scoop it. Keep in mind the colder the dough, the puffier the cookies will be and will need a few more minutes of baking time.
Using a cookie scoop drop equal-sized portions (1.5 tablespoons each) of the dough onto the baking tray, at least two inches apart. You could also use a spoon if you don't have a cookie scoop. See notes for baking frozen dough.
Bake for 12 minutes until the cookies are lightly browned on the edges and still puffy in the middle, rotating the tray halfway through the baking time to ensure even browning. Very gently, press down on each cookie with the back of a spoon or a metal spatula to flatten further if you like, then press a few extra chocolate chips onto the top of each cookie. Peanut butter gives the cookies slightly craggy edges so to smoothen them out, use the back of a spoon and gently press around the edges to get smooth, circular cookies while they're still hot. Cookies baked for 10 to 12 minutes are soft-baked, slightly gooey in the middle and they remain soft for a few days this way. You can also bake the cookies for 15 minutes if you prefer them a little firmer and they will be slightly drier than the soft-baked ones after a few days. See the third and fourth photo below for reference, the cookie on the right is under-baked.
Allow them to cool and firm up for 15 to 20 minutes, then transfer to a wire rack to cool completely. Store in an airtight tin at room temperature for 4 to 5 days. In the fridge, they'll last about 2 weeks and longer in the freezer. Happy baking!