Preheat the oven to 350°F (175°C) and line a baking sheet with parchment paper.
In a large bowl, use a hand mixer to cream together the room-temperature butter, brown sugar, and granulated sugar until light and creamy.
Add the vanilla instant pudding mix, vanilla extract, and eggs to the butter mixture and beat until fully combined and smooth.
In a separate bowl, whisk together the all-purpose flour, baking soda, and salt.
Add the dry ingredients to the wet ingredients and mix until just combined; do not overmix.
Stir in the 2 cups of semi-sweet chocolate chips until evenly distributed.
Drop rounded tablespoons of dough onto the prepared baking sheet, spacing them about 2 inches apart.
Press about 5–7 extra chocolate chips onto the top of each cookie dough mound.
Bake at 350°F for 8–9 minutes, or until the bottoms are just beginning to brown and the tops still look slightly underbaked.
Remove the cookies from the oven and let them cool on the baking sheet for 2 minutes, then transfer to a wire rack to cool completely.