Preheat the oven to 350°F. Line two large baking sheets with parchment paper or silicone baking mats and set aside.
In a medium bowl, whisk together flour, cocoa powder, baking soda, and salt and set aside.
Using a stand mixer fitted with the paddle attachment or a separate large mixing bowl with an electric mixer, cream the butter and sugars on high speed until light and creamy, 2-3 minutes. Do not skip this step. Add the chocolate pudding mix, vanilla, milk, and eggs, and beat on high for another 1-2 minutes 2-3, until the mixture is light and fluffy.
Slowly add half of the dry ingredients to the wet ingredients and turn the mixer on low to start so the flour doesn't get everywhere. Turn the mixer up to high speed and mix until combined. Add the rest of the dry ingredients and repeat until the dough is just combined. The cookie batter will be slightly sticky.
Pour the chocolate chips and chocolate chunks into the dough and mix on low speed until they're incorporated. If you have time, you can chill the dough for 1-2 hours, or up to 3 days, but it isn't necessary.
Use a very large cookie scoop, or 1/4 cup measuring cup to scoop the dough out and drop it on the prepared baking sheets. Roll the dough into balls, or tall cone shapes for extra thick cookies. Your hands will have chocolate on them, so coat them in bit of cocoa powder to help this or just wash them after you roll out all of the dough.
Arrange the cookie dough 3 inches apart on the cookie sheets and bake in the preheated oven for for 9-11 minutes, or until they're just set on the edges and top. Allow the baked cookies to cool on the baking sheet for 5 minutes then transfer them to a cooling rack to cool completely.