Preheat oven to 350°F (175°C). Line a baking sheet with parchment paper.
Beat butter and sugar on medium speed until light and fluffy, about 2–3 minutes. Add eggs and vanilla; mix until combined.
In a separate bowl, whisk flour, baking soda, cream of tartar, and salt. Add to the butter mixture on medium-low speed until a dough forms.
Fold in the sprinkles with a spatula.
Divide dough into 4 portions. Leave one plain; color the others pink, blue, and violet with gel food coloring.
Combine all doughs in one bowl and swirl gently - just 3–4 folds. Stop before the colors blend completely!
Scoop into balls and roll in granulated sugar. Place 2 inches apart on the baking sheet.
Bake 10–12 minutes until edges are just set. Cool on the pan for 5 minutes, then transfer to a wire rack.