Preheat oven to 350 degrees F. Line two baking sheets with parchment paper.
In a large bowl, beat the butter and sugars for 2-3 minutes until creamy and light. Add the eggs and vanilla and beat again, scraping the bottom and sides of the bowl.
Add the flour, baking soda, baking powder, and salt. Mix just until combined. Stir in 2 cups of the fruity pebbles and the white chocolate chips.
Use a large cookie scoop to scoop out approximately ½ cup mounds of dough and shape them into balls. Roll each ball of cookie dough in a shallow bowl filled with the remaining fruity pebbles.
Arrange the cookies on the prepared baking sheets, six to a sheet. Press them down to flatten to about 1-inch thick.
Bake for 11-13 minutes until set around the edges. Let cool on the pan for 5 minutes before transferring to a wire rack.
Meanwhile, make the frosting by beating the cream cheese until smooth.
Add the powdered sugar and marshmallow cream, then beat until creamy and smooth. Transfer to a piping bag fitted with a medium round tip or a large ziploc bag. Use scissors to snip off one corner for piping, if using the ziploc bag.
Once the cookies have cooled somewhat but are still warm, pipe the frosting on in swirls starting in the center and working out toward the edges. Sprinkle a few additional Fruity Pebbles on top for decoration.