Preheat oven to 375 degrees F. Line a couple of cookie sheets with parchment.
Whisk flour, baking soda and salt together in a bowl. Set aside.
Cream the butter, shortening and both sugars with an electric mixer, scraping sides of bowl often. Beat in the vanilla pudding. When well mixed, add the vanilla and eggs and beat until eggs are mixed in.
Add the flour mixture to the batter and stir until it is almost fully mixed in. Add oats and continue stirring until flour disappears. Stir in chocolate chips.
Drop batter by (heaping!) tablespoons, spacing about 2 ½ inches apart, onto the parchment lined cookie sheets. Bake cookies for 12 minutes or until edges are brown and tops appear set. Let cool on sheets for about 5 minutes, then transfer to a wire rack to continue cooling.
You can use heaping teaspoons and get about 60 cookies (bake time will be shorter), but I've made these several times since first posting and prefer using heaping tablespoons. Heaping tablespoons will give you about 32 to 35 cookies.