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Using your beaters or a mixer, beat together yogurt, butter and sugar until combined and light in color.
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Stop your mixer and scrape down the sides of the bowl. Add eggs, one at a time. Add vanilla. Scrape down your bowl again.
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In a separate bowl, combine flour baking powder and soda, cornstarch and salt. Mix to combine. Slowly add flour mixture to wet ingredients. Mix until completely combined.
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Cover and refrigerate dough for at least 30 minutes.
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Preheat oven to 350 degrees. Line 2 baking sheets with parchment paper or spray with nonstick cooking spray.
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Scoop out 1 inch balls and place them 2 inches apart on the cookie sheet.
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Bake for 10 minutes.
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Allow to completely cool before frosting.