Whisk together the flour, baking powder and salt in a medium bowl.
Beat the butter and sugar in a stand mixer fitted with the paddle attachment on medium-high speed until fluffy, about 3 minutes. Add the egg and beat until combined, scraping down the bowl as needed. Add the vanilla and beat to combine.
With the mixer on low speed, gradually add the flour mixture and beat until incorporated. Transfer half of the dough to a medium bowl. Add 4 to 5 drops of the blue gel food coloring to the remaining dough and mix on low until combined.
Use an ice cream scoop or large spoon to drop spoonfuls of the cookie dough into a medium bowl, alternating the colors, until all the dough has been scooped. Cover and freeze until firm, about 20 minutes.
Line 2 baking sheets with parchment paper. Scoop 12 balls of dough (about 1/4 cup each) with a large ice cream scoop or a measuring cup onto the prepared baking sheets, spacing the dough 2 inches apart.
Flatten each portion of dough and put a marshmallow half in the center. Fold up the cookie dough, pinching to seal, so that the marshmallow half is completely sealed. Roll into a smooth ball and roll the top in the sprinkles. Repeat with the remaining cookie dough. Refrigerate until firm, about 15 minutes.
Meanwhile, preheat the oven to 375 degrees F.
Bake the cookies until lightly golden around the edges, 15 to 20 minutes. (If marshmallow cracks through the top, no need to worry! It will settle back down as it cools). Let cool 5 to 10 minutes on the baking sheets.
When measuring flour, we spoon it into a dry measuring cup and level off excess. (Scooping directly from the bag compacts the flour, resulting in dry baked goods.)
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