Preheat the oven to 350 F. In a large bowl, mix butter and sugar together 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 place onto a large ungreased baking sheet. Bake for 10-12 minutes. Place the powdered sugar into a shallow dish. Roll each cookie into the powdered sugar.