Preheat your oven to 350°F (175°C). Line a baking sheet with parchment paper or a silicone baking mat to prevent sticking and ensure even baking.
In a large mixing bowl, cream together the butter, sugar, and brown sugar until the mixture is light and fluffy. This should take about 3-4 minutes using an electric mixer.
Beat in the eggs, one at a time, ensuring each is fully incorporated before adding the next. Then, add the milk and vanilla extract, mixing until well combined.
In a separate medium-sized bowl, whisk together the flour, baking soda, baking powder, and salt. Gradually add this dry mixture to the wet ingredients, mixing on low speed or by hand until just combined.
Stir in the rolled oats, bittersweet chocolate chips, milk chocolate chips, and chopped walnuts by hand until evenly distributed throughout the dough.
Using a cookie scoop or a spoon, drop 1-inch balls of dough onto the prepared baking sheet, spacing them about 1 1/2 inches apart to allow room for spreading.
Place the cookies in the preheated oven and bake for 10-13 minutes, or until the edges are golden brown and the centers are just set.
Allow the cookies to cool on the baking sheet for 1-2 minutes before transferring them to a wire rack to cool completely.