Preheat the oven to 350 degrees.
Combine cake mix and flour in a medium bowl, whisk {or sift} together. Add eggs, melted butter and sour cream. Mix using a hand held {or stand} mixer until you have a thick dough. Add Fruity Pebbles and chopped white chocolate {or white chocolate chips} to cookie dough and mix until they are evenly distributed in the dough.
Using a large cookie scoop, measure out 12 cookies. Use your hands to press the cookie dough into a circle that is a thick round disc. Bake 8 cookies at a time. Place the cookie on a silicone mat {or parchment} lined baking sheet for 9-11 minutes or until set.
Remove cookies from the oven and allow them to cool completely on the baking sheet.
While the cookies are cooling, start making the frosting. In a medium bowl combine the softened cream cheese, softened butter, powdered sugar, vanilla extract and milk. Mix using a hand held {or stand} mixer until thick but spreadable. Add more milk if needed.
Spread the frosting on top of each cookie or add the frosting to a piping bag and pipe the frosting on the top of each cookie. Add additional Fruity Pebbles to the edge of each cookie on the frosting and serve.
Store in an airtight container in the refrigerator for up to 4 days or freeze for up to 3 months.