Preheat the oven to 375℉, and line 3 cookie sheets with parchment paper.
In the bowl of a stand mixer fitted with the paddle attachment, cream the butter and the sugar on medium speed for 3 minutes, until light, fluffy, and pale in color.
Turn the mixer down to low, and add the eggs one at a time, along with the vanilla extract.
Add the flour, pudding mix, salt, and baking soda. Mix until mostly combined, but streaks of flour are still showing. Then stir in the chocolate chips.
Scoop cookie dough into mounds 1 1/2 tablespoons in size, onto the cookie sheets, spaced 2 inches apart.
Next, using two fingers or the back of a tablespoon, lightly indent the center of the cookie dough. This will allow the cookies to spread evenly and cook evenly.
Bake at 375℉ for 8-10 minutes until the cookies are puffed and just starting to brown around the edges.
Remove the cookies from the oven and immediately use the lid of a jar or a large round cookie cutter to mold the cookie edges into a circle. Do this while the cookies are still hot. This will give your cookies crisp edges and a soft and fudgy center.
Repeat the baking and shaping process until all the cookie dough is baked.
Allow the cookies to cool on the pan until set enough to pick up. Store in an airtight container for 4 days.