Step 1: Preheat your oven to 350°F (175°C) and grease an 8x8 inch baking pan or line it with parchment paper for easy removal.
Step 2: In a large mixing bowl, cream together the softened butter, creamy peanut butter, granulated sugar, and brown sugar until the mixture is light and fluffy.
Step 3: Add the egg and vanilla extract to the creamed mixture, beating well until fully incorporated.
Step 4: In a separate bowl, whisk together the all-purpose flour, baking soda, and salt.
Step 5: Gradually add the dry ingredients to the wet ingredients, stirring until just combined. Be careful not to overmix the dough.
Step 6: Fold in 3/4 cup of the chocolate chips by hand.
Step 7: Press the dough evenly into the prepared baking pan using a spatula or clean hands.
Step 8: Sprinkle the remaining 1/4 cup of chocolate chips over the top and lightly press them into the surface.
Step 9: Bake for 22-25 minutes, or until the edges are lightly golden brown but the center still appears slightly soft.
Step 10: Allow the bars to cool completely in the pan before cutting into squares for the best texture.