Preheat the oven to 350 F. In a large bowl, combine butter with powdered sugar until fluffy. Add in the vanilla extract, and mix until smooth. Add in the flour, mix until it is fully combined.
Fold in the cocoa pebbles cereal. Roll the cookie dough into balls, and flatten each one slightly. Place onto a large ungreased baking sheet. Bake for 10-12 minutes.