Mix the powdered sugar, and cardamom together in a small bowl.
In a large bowl or a stand mixer bowl with the paddle attachment, beat room temperature butter until smooth with an electric mixer at medium speed.
Beat in the egg and rose water until blended. The mixture will look watery.
With the mixer on low beat in the powdered sugar mixture for two minutes.
With the mixer on low speed beat in the rice flour until a stiff dough forms.
Remove dough from bowl and place on a floured piece of plastic wrap or parchment paper. Shape the dough with your hands to make a rectangle then using a rolling pin shape the dough into a rectangle 4" wide by 8" long and ¼" thick.
Using a bench scraper reform the sides of the dough to make them nice and straight. You may have to reroll the dough to get it the correct size.
Place the rose petals on a cutting board and chop with a knife to make small pieces. You will want about ¼.
Sprinkle the rose petals over the dough and then press the petal into the dough. Gently roll over the top of the rose petals with a rolling pin to get the petals to stick to the dough.
Wrap the dough in plastic wrap or parchment paper that the dough is sitting on and chill for at least 2 hours or overnight.
When ready to bake heat your oven to 300° F.
Remove dough from the wrap and set it on a cutting board. Cut the dough in half lengthwise then cut into 22 - ¾" logs.
Transfer the cookies to a parchment-lined baking tray and bake for 20 - 25 minutes or until the bottoms are golden brown. The rose petals will darken as they bake, but they will still be pretty.
Store the cookies in an airtight container for up to two weeks.