Preheat the oven to 375° F. Line a rimmed baking sheet with parchment paper and set aside.
In a large bowl, whisk together the flour, sugar and salt. Create a well in the center of the dry ingredients and add the butter, mix with a spoon until combined. Scatter the pistachio pieces over the dough and knead with hands until the dough comes together and is smooth. Wrap tightly with plastic wrap and chill for at least 10 minutes.
*(This dough is a bit coarse/crumbly, and will need to be kneaded together and formed by hand. If the dough if too crumbly to form into a disc for chilling, you can add up to 1 TBSP water, a but at a time, to get it to bind. If your pistachios aren;t chopped finely as noted, that could also be a problem.)
Remove dough from refrigerator and place between two sheets of parchment paper. Roll dough to about 1/4 inch thickness and cut out cookies with a 1 1/2 inch round cutter, and place them on the lined baking sheet. Artfully place the flowers or individual petals on the cookies and press gently into the dough.
Bake on the center rack of the oven for 10-12 minutes, until the edges turn slightly golden. Remove from the oven and sprinkle immediately with sugar, then allow to cool.