Prep equipment: Preheat the oven to 375°F. Line two baking sheets with parchment and set aside.
Mix dry ingredients: In a large bowl, whisk together flour, baking soda, and salt and set aside.
Brown butter: In a heavy-bottomed saucepan over medium heat, melt half the butter (6 tablespoons). Swirl until it starts to turn a light amber color. Be careful! The butter can burn very easily. Pour butter from the pan into a large glass bowl to cool. Once the butter has cooled slightly, add in the remaining butter to melt together.
Make cookie batter: Whisk brown sugar, granulated sugar, egg, and egg yolks into cooled melted butter until smooth. Whisk in vanilla extract. Add dry ingredients to wet ingredients and fold the batter together. Fold in the dark chocolate and Cadbury eggs; do not overmix. Refrigerate dough for 30-60 minutes.
Bake: Scoop 2- to 3-tablespoon balls of cookie dough and place onto prepared baking sheets. Bake cookies for 8–10 minutes, or until edges are golden brown. Cookies will continue to cook outside of oven; do not overbake.
Cool: Let cookies cool on the pan for 10 minutes before transferring them to a wire rack to cool completely.