Combine the flour, baking powder, baking soda, and cornstarch in a medium bowl. Give it a good whisk until well mixed, then set the bowl aside.
In a large bowl, combine the muscovado sugar and room temperature butter. Use a handheld mixer to blend them together at medium-high speed for about 2 minutes.
Add the room temperature yogurt and vanilla extract to the butter mixture. Blend with the handheld mixer at medium-high speed for 30 seconds to one minute.
Combine the dry ingredients with the wet ingredients. Use a handheld mixer on medium-low speed to blend until no traces of flour remain.
Scoop the cookie dough balls. Each cookie is 3 tablespoons of dough. Scoop all 18 cookie dough balls and place them on a parchment lined pan. Cover the dough balls and place the pan in the refrigerator while the oven preheats.
Pre-heat the oven to 350 degrees F and line 2 cookie sheets with parchment paper. Place the rolling sugar in a small bowl.
Once the oven is preheated, take the dough balls out of the fridge. Roll them gently between your palms until they are smooth, then roll them in sugar to coat. Arrange 4 to 5 sugar-coated dough balls on a parchment-lined baking sheet, keeping the rest of the dough balls in the refrigerator until ready to bake.
Bake the cookies for 15 minutes. Once out of the oven, let the cookies rest on the pan for 5 to 10 minutes before transferring them to a cooling rack.
Store the cookies in an airtight container at room temperature.