Start by beating butter and sugars together for 1-2 minutes until very fluffy. Add vanilla and egg and mix well. In a separate bowl whisk together flour, pudding mix, baking soda, and salt. Add dry ingredients to wet ingredients and mix until incorporated and dough comes together. Stir in chocolate chips. Cover tightly and chill for at least 1 hour.
After you put the dough in the fridge to chill, prepare the hot fudge sauce. Line a small baking sheet (or something similar that is flat and will fit in your freezer) with foil, parchment, or wax paper. Drop your heaping teaspoons of hot fudge onto the paper. (see note) Freeze until ready to use (no need to cover).
Roll your dough into 14 balls (yes, they are large!) Take the hot fudge drops out of the freezer. Take one dough ball and use your fingers to break it in half. Place a hot fudge drop in the middle of one half of the dough ball, then top it with the second half and roll the ball in your hands to make it round again and seal the sides so you can no longer see the fudge. Place on prepared baking sheet and repeat with remaining dough. (Careful not to crowd your cookies because they will spread and they are big. About 6 to a large baking sheet is plenty)
Bake cookies for 9-12 minutes until they are started to lightly brown around the edges but aren't quite fully cooked. Remove them from the oven and allow to cool for about 20 minutes on the pan (until the pan cools), then transfer the cookies to a wire rack to cool completely - they are completely done cooling when you can touch one of the chocolate chips and it is firm. Store in airtight container. Serve at room temperature or reheat for a few seconds in the microwave for a warm and melty treat! (see note)