In a large mixing bowl, combine the room temperature cream cheese and granulated sugar. Using an electric mixer, beat until smooth and creamy. This should take about 2-3 minutes.
Add in the peanut butter and vanilla extract to the cream cheese mixture. Mix until fully combined and creamy, scraping down the sides of the bowl as needed.
Gently fold in the whipped topping using a spatula. Be careful not to overmix; you want to maintain that light and fluffy texture.
Once the whipped topping is fully incorporated, add the Cocoa Pebbles and chocolate chips to the mixture. Gently fold them in until evenly distributed.
Pour the mixture into a 9x13 inch baking dish, spreading it out evenly. Use your spatula to smooth the top.
Cover the dish with plastic wrap and place it in the refrigerator for at least 4 hours, or overnight if you have the time. This will help the dessert set up nicely.
Before serving, sprinkle additional Cocoa Pebbles on top for garnish. Cut into squares, serve, and enjoy your Peanut Butter Cocoa Pebbles No Bake Dessert!