In the bowl of a stand mixer (or a large bowl with a hand mixer), cream together the butter and sugars until light and fluffy, 3-4 minutes.
Add eggs and vanilla and beat until smooth.
In a separate medium bowl, whisk together flour, baking powder and salt.
With mixer on low, gradually mix in the flour mixture until just combined (taking care not to over-mix).
With a wooden spoon, gently stir in the Fruity Pebbles cereal until just combined.
Chill dough in refrigerator for about 15 minutes. While dough is chilling, preheat oven to 350 degrees and 2 line 2 cookie sheets with parchment paper or Silpats.
Using about 2 Tbsp dough at a time, drop rounded cookie dough on prepared baking sheets. I recommend using a cookie scoop for dropping dough- this is a great set with various sizes (affiliate link).
Bake for about 10-12 minutes until just golden around edges. Let cookies cool on baking sheet for 5 minutes before moving to wire racks to cool completely.