In a mixing bowl, combine flour, rose petals, cardamom, and salt, and set aside.
With an electric mixer, beat together the butter and sugar until creamy.
Beat in the rosewater and then gradually mix in the flour mixture.
Shape the dough into a disc, wrap in cling wrap, and chill for at least two hours and up to two days.
When ready to bake, preheat the oven to 300°F (150°C) and line two baking sheets with parchment paper.
On a floured surface, roll out the dough to a ¼ inch (6mm) thickness, cut out circles with a 2-inch (5cm) cookie cutter, and place on your prepared baking sheets. Gather and reroll any scraps.
With a skewer, prick a few holes in each cookie.
Bake for about 25 minutes, until the edges of the cookies are just barely starting to color. Let cool in wire racks.
Enjoy freshly baked with a cup of tea. Store leftover cookies in an airtight container at room temperature for up to 1 week.