In a large mixing bowl, add the flour, baking powder, granulated sugar, and salt. Mix briefly until blended.
In a medium bowl, whisk together the eggs, milk, half and half, vanilla extract, and melted butter.
Add the wet ingredients to the dry ingredients. For fluffy pancakes, briefly mix until blended taking care not to over mix the batter. The pancake batter will be thick with some small lumps, which is perfectly fine.
With a silicone spatula, slowly, gently, carefully fold the rainbow sprinkles into the pancake batter until just incorporated. Do not stir as this may cause the colorful sprinkles to bleed into the batter. Allow batter to rest while the griddle heats up.
Generously butter a pancake griddle. Place it on your stovetop over medium heat. Once the butter is melted and hot, ladle the pancake batter onto your griddle using a 1/4 measuring cup. Allow the pancakes to cook undisturbed for approximately one minute.,
When the sides of the pancakes begin to look cooked AND you see small bubbles rising to the surface, quickly flip the pancakes over. Allow the pancakes to continue cooking until done.