Combine the all-purpose flour, baking powder, and baking soda in a bowl, stirring until the leavening agents are evenly distributed.
In a separate large mixing bowl, beat the softened butter with the granulated sugar for several minutes, continuing until the mixture appears pale, light, and fluffy.
Blend in the lightly beaten egg and vanilla essence until they are fully incorporated.
Add the flour mixture gradually, alternating it with portions of Greek yogurt. Mix only until the ingredients come together into a smooth but noticeably sticky dough.
Cover the dough securely with plastic wrap and refrigerate it for a minimum of 2 hours.
Preheat the oven to 350°F (175°C).
Take half of the chilled dough from the refrigerator, leaving the remaining portion cold until needed.
Lightly flour the work surface, then roll out the dough to a moderately thick layer rather than making it excessively thin.
Cut the dough with a large round cookie cutter and arrange the shapes on a baking sheet, leaving adequate space between each cookie.
Place the baking sheet in the preheated oven and bake for 10–12 minutes.
Remove the cookies while they are still relatively soft and before they develop significant browning.
Repeat the rolling, cutting, and baking process with the remaining refrigerated dough.
Transfer the baked cookies to a wire rack and allow them to cool completely before applying the frosting.
Beat the softened butter in a bowl for several minutes until it becomes light and fluffy.
Add the sifted powdered sugar little by little while continuing to beat the mixture until the frosting is smooth.
If necessary, incorporate a small amount of milk to modify the frosting consistency. Blend in food coloring as desired until the preferred shade is achieved.
After the cookies are entirely cool, spoon a generous amount of buttercream onto each one and spread it evenly across the surface.
Decorate the frosted cookies as desired, then allow the buttercream to set before serving.