Preheat your oven to 350°F. Line a baking sheet with parchment paper.
Add your room temperature butter into a stand mixer or large bowl. Now add in the brown sugar and white sugar. Mix on high for about one minute, just until everything is combined.
Add your whole egg into the butter and sugar mixture and mix it on low. While it is mixing, add in the egg yolks one at a time, and add the vanilla extract. Mix it for about one minute, until it is incorporporated
In a separate bowl, combine the dry ingredients, including the flour, baking soda, and salt. Slowly add the the dry ingredients into the wet ingredients while mixing on low speed.
Once all of the dry ingredients are added, continue to whisk on low until everything is fully incorporated. The mixture should be a cookie dough batter now.
Pour the milk chocolate chunks, the semi sweet chocolate chips, and walnuts into the cookie dough. Use a spoon or a spatula to gently fold the chocolate into the batter.
Use a cookie scoop to scoop out cookie dough balls. Place the dough balls on the parchment paper. Leave 1-2 inches between each cookie because they will spread.
Place the cookie sheet in the oven and bake them for 7-8 minutes. Remove the cookies from the oven and use a spatula to transfer them to a cooling rack.
Continue baking the cookies until all of your batter is used up.