Preheat the oven to 350 degrees F. and line a baking sheet with parchment paper or a baking mat.
In a large bowl (or the bowl of your stand mixer) beat together the butter, peanut butter, granulated sugar, and brown sugar, until the mixture is light and fluffy, about 5 minutes (using a hand mixer if you don't have a stand mixer is a good option.)
Add the two eggs and vanilla and mix to combine.
Add the oats, flour, baking soda, baking powder, and salt to the bowl and mix to combine well.
Let the mixture rest for 5 minutes and then stir again (this gives the oats time to absorb some of the moisture giving you the nice cookie dough texture).
Using a cookie scoop or two spoons, place a large tablespoon of dough on the baking sheet, about 3 inches apart.
Bake cookies for 10-12 minutes, until the edges are set and lightly golden brown.
Remove from the oven and let cool on the baking sheet for 5 minutes before removing from the sheet and placing on a wire rack to cool.
Enjoy right away. Store extras in an air-tight container for up to a week or in the freezer for much longer.
Notes
Butter is the best for cookies. It adds great flavor and helps the texture to be nice and crisp
For cookies that will be eaten in a day or two, store soft cookies in a container with a tight-fitting cover.
Both granulated and brown sugars are great and add color and flavor to the finished cookies
The key to keeping cookies fresh and soft is to seal them in an airtight container, like a resealable freezer bag. And here's a nifty little trick: add a piece of bread to the bag.