In a large mixing bowl, cream together the butter (or ghee, if using), sugar, lemon zest, dried rose petals, and vanilla until light and fluffy, about 3-5 minutes.
Add the flour and beat until combined, and the dough forms a ball.
Generously flour a flat surface and roll out your doll to 1/4 inch thickness. Use cookie cutters of your preferred shape to cut out the dough and carefully transfer to a parchment lined baking sheet.
Cover the baking sheet with plastic wrap and freeze until firm (10-20 minutes). Roll out the leftover scraps, and repeat with the remaining dough.
Preheat the oven to 350 degrees. Bake the cookies on the middle rack of the oven for 12-14 minutes or until just lightly golden. Let cool on the baking sheet 5 minutes, then transfer to a wire cooling rack to cool completely.
To make the glaze:
In a small bowl, combine yogurt, brown sugar and lemon juice. Stir until smooth.