Line baking sheets with parchment paper. Set aside.
In the bowl of a stand mixer with a paddle attachment (or using a handheld mixer), beat the butter on medium-high speed until smooth (about 1 minute).
Add the peanut butter and beat until combined and creamy, about 2 minutes.
Add the brown sugar and cream together on medium-high speed until smooth, about 2 minutes.
Add the eggs one at a time, mixing for about 30 seconds after each addition. Scrape down the sides of the bowl as needed and mix briefly to combine.
With the mixer off, add the flour, oats, baking soda, and salt. Mix on low until just combined, being careful not to overmix.
Using a 2-tablespoon scoop, drop rounded portions of dough onto the lined baking sheets about 2 inches apart.
Place the baking sheets of unbaked cookies into the refrigerator to chill for about 30 minutes. (If letting the dough chill overnight, be sure to cover.)
When ready, preheat the oven to 350°F. Remove the cookie dough from the refrigerator.
Bake for 10 minutes, or until the edges are lightly browned and the centers still look soft.
Remove from the oven and let cookies cool on the baking sheet for a few minutes before transferring to a wire rack to cool completely.