Add the white and brown sugar and the butter to a standing mixer bowl.
Mix on low until combined and then turn the speed up to high and whip for 2 minutes until light and fluffy.
Stir in the peanut butter, eggs and vanilla on low speed until combined.
Add the soda, salt, flour, and oats to the bowl. Turn the speed on low and mix until just combined.
Press the dough into a greased and parchment paper-lined 9x13 pan. Bake for 25-30 minutes.
Remove and allow the bars to cool inside the pan.
Frosting
In a medium bowl, add the powdered sugar, butter, and cream. Mix on low until combined, then turn up the speed to high and whip for 2 minutes until light and fluffy.
Spread the frosting all over the top of the bars & enjoy!