Preheat the oven to 350 F.
In a large bowl, cream together the peanut butter, butter and sugars using a hand mixer (or a stand mixer), until soft and creamy.
Add the egg and vanilla extract and continue to mix until fully combined.
In a separate bowl, whisk together the flour, baking soda and salt. Add these dry ingredients to your large bowl slowly, continuously mixing using your mixer.
Scoop out 1-2 tablespoons of dough and roll into 1-inch balls, and then flatten into a disc (this helps prevent it from cracking). If it cracks, smooth out the cracks with you hands. Place the cookies on a half sheet baking pan lined with a silicone mat or parchment paper. Use a fork to press down on each ball of dough to create a criss-cross pattern and slightly flatten it more.
Bake for 8-10 minutes or as soon as tops begin to slightly crack. To keep them soft and chewy, be careful to not overbake. Let cool on the baking sheet for a few minutes and then transfer to a wire cooling rack.
