Preheat your oven to 350°F (175°C). Line two large baking sheets with parchment paper or silicone baking mats.

In a medium bowl, whisk together the all-purpose flour, baking soda, and salt. Set aside.

In the bowl of a stand mixer fitted with the paddle attachment (or using a large bowl and a hand mixer), beat the softened butter, peanut butter, granulated sugar, and brown sugar on medium speed until the mixture is light and creamy, usually about 3 to 4 minutes. Stop and scrape down the sides of the bowl as needed.

Add the eggs one at a time, mixing well after each addition until just combined. Be careful not to overmix at this stage. Stir in the vanilla extract.

With the mixer on low speed, gradually add the dry flour mixture to the wet ingredients. Mix only until the flour streaks have almost disappeared.

Fold in the old-fashioned rolled oats using a rubber spatula or mix on very low speed until the oats are evenly distributed throughout the dough.

Scoop the cookie dough using a standard 1.5-tablespoon cookie scoop (or roll into golf-ball sized portions) and place them about 2 inches apart on the prepared baking sheets.

Optional Step: For the traditional peanut butter cookie appearance, gently flatten each dough ball with the tines of a fork in a criss-cross pattern.

Bake for 10 to 12 minutes. The edges of the cookies should be lightly golden brown and set, but the centers should still look slightly soft when removed from the oven.

Allow the cookies to cool on the baking sheet for 5 minutes before carefully transferring them to a wire rack to cool completely. Store airtight at room temperature.