Preheat oven to 350 degrees. Line two to three baking sheets with parchment paper and set aside.
Cream butter, shortening, brown sugar and granulated sugar together to cream. Add in vanilla and eggs and mix again until lighter in color and fluffy. Scrape the sides and bottom of the bowl and mix again to ensure an evenly mixed batter.
Add in your measured flour (see notes below), salt and baking soda. Stir until just combined. Scrape the sides and bottom of the mixer to ensure the batter is evenly mixed. Add in the chopped cadbury eggs and stir in by hand.
Using a 3 tablespoon cookie scoop, portion out cookies onto your baking sheets. Top with more cadbury eggs, if desired.
Bake cookies 8-10 minutes. Cool 2-3 minutes on the hot baking sheet before transferring to cooling rack.
How to measure flour: if you store your flour in the bag you get from the store or a canister on the counter, be sure to stick a whisk into the flour, stir it around a few times to aerate. It should be easy to scoop a measuring cup through. Scoop to overfill the measuring cup and level the top with the flat side of a butter knife. To get Flat Cookies, reduce the flour used to 2 1/2 cups. If you notice your cookies are too flat and you'd like them to hold their shape a little more, like in the pictures in this post, stir in a little extra flour by hand.