Preheat oven to 350 degrees.
In a large bowl (or if using a stand mixer, in that bowl), place the butter and the two sugars. Beat well for about 3 minutes, until lighter in colour and soft and fluffy
Crack the eggs and add them, and beat for about another minute. Add the vanilla and beat to combine.
Add the peanut butter and beat until incorporated.
Add the dry ingredients, and start slowly beating them in (be careful because the flour will fly if you start too high). Once everything is incorporated, stop beating and remove the bowl.
Scoop the cookies out into balls and use a fork to create a crosshatch pattern on the top.
Bake in the preheated oven for about 10-12 minutes, until the edges are brown. Remove from the oven and allow to cool for about 5 minutes on the cookie sheet, and then remove to a wire rack to cool completely.
Store in an air tight container at room temperature for up to a week, or freeze for up to 3 months.