Preheat your oven to 350°F. Line a baking sheet with parchment paper or a silicone baking mat. Set aside.
In a mixer or large bowl, beat together the peanut butter and the brown sugar. Mix in eggs one at a time. Next, add in the vanilla.
Add in the flour, salt, and baking soda. Mix until all of the ingredients are completely combined. The dough should come together really well, and be one big ball of dough.
Roll dough into roughly 1 ½-2 inch balls, and spread them a few inches apart on a baking sheet lined with parchment paper or a baking mat.
With a fork and a glass of warm water, make the crisscross pattern on the cookies. Dip the fork in the warm water and shake off excess water. Gently press the fork down on the top of a ball of dough, leaving fork lines. Gently press the fork down again in the opposite direction, creating a grid-like pattern on the top of the cookie. Repeat this step for each cookie. The dough ball will flatten a bit, but that's okay.
Bake the cookies for 12-13 minutes. The edges will just be starting to turn golden. The cookies will still seem pretty soft, but they will set and firm up more as they cool. Let them rest for about 2 minutes, then transfer them to a cooling rack.