Prep: Line a small baking sheet with baking paper (small enough to fit in your refrigerator), set it aside.
Make dough: In a large bowl or bowl of your stand mixer, cream butter and sugars together until light and fluffy. This takes a few minutes.
Add egg and egg yolk and mix until well combined. Whisk in salt and baking soda, then mix in flour (using low speed) just until combined (you don’t want to overmix). The batter will be very thick. Fold in chopped mini eggs with a spatula.
Using a cookie scoop (see notes for size), scoop the dough into 14 large balls and place them on the prepared baking sheet one next to the other. Pat each one down so that you get disks instead of balls, each one about 2 inches (5 cm) wide. Take the few extra mini eggs, slice them in half and stick them on top of the cookies. Place the cookies in the refrigerator and chill until hard, about one hour.
When you are ready to bake, preheat your oven to 350°F (175°C). Place cookies on a parchment-lined baking sheet, about 3 inches (8 cm) apart. Bake in the middle of the oven for 16-19 minutes, until the tops and sides look golden brown. (You will have to bake several trays because of the size of the cookies.)
Remove cookies from the oven and allow them to cool on the sheet for 10 minutes, then transfer them to wire racks to cool completely. They will be very soft when hot from the oven, but will set as they cool. Keep cookies in an airtight container at room temperature.