Position rack in center of oven and preheat to 350°F. Generously butter a 12x18x1-inch rimmed baking sheet. Set aside.

In a very large bowl (using a spoon or electric mixer), mix together the eggs and sugars until well-combined. Beat in the salt, vanilla, peanut butter, and butter until smooth. Stir in the baking soda (make sure there aren't any lumps) and the oats, then add the M&Ms, chocolate chips, and peanut butter chips and mix until just combined.

Spread the batter into the prepared baking pan, pressing down and smoothing the top into an even layer. Bake for 18 to 22 minutes or until edges are very light golden brown and center is set. Allow to cool in the baking pan before slicing and serving.