Preheat oven to 350 degrees and spray two 8×8 baking pans lightly with cooking spray (if you only have one 8X8 pan, you can bake cookies one at a time).
Cream butter and sugar together in a stand mixer (or in a bowl with a hand mixer) until light and fluffy. Add egg and vanilla and mix to combine.
In a separate bowl, whisk together the flour, baking soda, cream of tartar and salt.
Pour the flour mixture into the wet mixture and mix until just combined, taking care not to over-mix. Gently stir in the rainbow sprinkles.
Divide cookie dough in two and press into the bottoms of the prepared pans.
Bake for 10-12 minutes, until edges are just browning. Remove from oven and let cookies cool in the pan.