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 peanut butter. Beat for about 2 minutes, or until smooth.
Add brown sugar and cream on medium-high speed for 2 minutes, until smooth.
Add eggs, one at a time, mixing for 30 seconds after each addition. Scrape down the sides of the bowl and mix again if needed.
With the mixer off, add flour, oats, baking soda, and salt. Mix on low until just combined, being careful not to overmix.
With the mixer still on low (or by hand), add the M&M's, chopped peanut butter eggs, and chocolate chips. Mix until incorporated. (If using an electric mixer, only mix for a few seconds.)
Using a 2-tablespoon scoop, drop dough onto the lined baking sheets about 2 inches apart. Top with extra Easter M&M's (optional).
Chill the dough in the refrigerator for 30 minutes. (If chilling overnight, cover the dough.)
When ready, preheat the oven to 350°F. Remove dough from the refrigerator.
Bake for 10 minutes, or until the edges are lightly browned and the centers still look soft.
Let the cookies cool on the baking sheet for a few minutes, then transfer to a wire rack to finish cooling.