Cream the butter and sugars: In a large mixing bowl or stand mixer, cream together the softened butter, brown sugar, and white sugar for 2–3 minutes until fluffy.
Add eggs and vanilla: Beat in the eggs one at a time, then stir in the vanilla extract.
Mix dry ingredients: In a separate bowl, whisk together the flour, baking soda, salt, and oats. Gradually add this mixture to the wet ingredients until just combined.
Fold in the chocolate: Gently mix in the milk chocolate chips and dark chocolate chunks. Reserve a few for topping if desired.
Chill the dough: Cover and refrigerate the dough for at least 2 hours (or overnight for best results).
Preheat and scoop: Preheat oven to 350°F (175°C). Scoop dough into large balls (about 3 tbsp) and place them 2–3 inches apart on a parchment-lined baking sheet.
Bake: Bake for 11–13 minutes, until edges are set but centers are still soft. Do not overbake!
Cool: Let cookies cool on the pan for 5–10 minutes before transferring to a wire rack. Enjoy warm!