Preheat your oven to 350 degrees Fahrenheit and line two cookie sheets with parchment paper. Set aside.
In a medium bowl combine flour, cocoa powder, baking soda and salt. Whisk quickly to combine and set aside.
In a bowl of an electric mixer fitted with a paddle attachment over medium/high speed, mix the unsalted butter and sugars until light and fluffy, about 3 minutes. Add eggs one at a time beating well after each addition. Add in the vanilla extract, followed by the chocolate pudding mix and beat for a minute or so until combined. Stop and scrape the mixer to incorporate ingredients.
Turn the speed to low and add the flour mixture, mixing until just combined. Remove bowl from mixer and fold in the chocolate chips.
Wrap the bowl with plastic wrap and chill the dough for at least 30 minutes.
Using a medium sized cookie scoop, scoop spoonfuls of dough on the parchment lined cookie sheet, spacing them at least 2 inches apart. Place in the oven and bake cookies for 9-10 minutes.
Remove cookies from the oven and allow to cool for about 5 minutes, transfer the cookies to a wire rack, stud the surface with additional chocolate chips. Allow the cookies to cool completely.