Step 1: Preheat your oven to 350°F (175°C). Line a 9x13-inch baking dish with parchment paper, leaving an overhang on the sides for easy removal, or simply grease the dish well.
Step 2: In a large mixing bowl, combine the softened ½ cup unsalted butter and ½ cup granulated sugar. Beat them together with an electric mixer until the mixture is light, pale, and fluffy.
Step 3: Crack in 1 large egg and add 1 teaspoon of vanilla extract to the creamed mixture. Continue beating until everything is well combined and smooth.
Step 4: Stir in the 1 (3.4 oz) box of instant pistachio pudding mix. Next, gradually add 1 ½ cups all-purpose flour, ½ teaspoon baking soda, and a pinch of salt. Mix until a soft, cohesive dough forms.
Step 5: Press the prepared dough evenly into the bottom of your 9x13-inch baking dish. Use a spatula or the back of a spoon to ensure a smooth, uniform layer all the way to the edges.
Step 6: Place the dish in your preheated oven and bake for 15-18 minutes, or until the edges are lightly golden and a toothpick inserted into the center comes out clean. The center should still feel slightly soft to the touch. Remove from the oven and allow the cookie base to cool completely in the pan before frosting.
Step 7: While the cookie base cools, make the frosting! In another large bowl, beat together 1 (8 oz) package of softened cream cheese and ¼ cup of softened unsalted butter until smooth and creamy.
Step 8: Add 2 cups of powdered sugar and 1 teaspoon of vanilla extract to the cream cheese mixture. Beat until light, fluffy, and completely smooth. If the frosting seems too thick, add milk, 1 tablespoon at a time, until you reach your desired spreadable consistency.
Step 9: Once the cookie base is fully cooled, spread the creamy pistachio frosting evenly over the top. Use a spatula to create a beautiful, smooth layer. For clean slices, chill the frosted bars in the refrigerator for at least 30 minutes to an hour to allow the frosting to set.
Step 10: After chilling, lift the bars out of the pan using the parchment paper handles (if you used them). Using a sharp knife, cut them into squares. Serve immediately.