Put the sugar and soft butter into the bowl of a food processor and pulse to combine completely.
Add the flour and extract, and pulse about 10 times, then run the machine briefly, just until the dough comes together into a lump or lumps.
Turn the dough out onto a floured surface and bring together into a smooth flat disk. Wrap in plastic and refrigerate until firm enough to roll, about 2 hours.
While the dough is chilling, remove the stems from the pansies, and place them on a large sheet of waxed paper, or parchment paper. Place another sheet on top, and then weigh it down with a baking tray or other large flat surface, topped with several heavy books. Let the pansies press for at least 30 minutes, or overnight if you like.
Meanwhile, preheat the oven to 325F
Roll out the dough to a 1/8 to 1/4 inch thickness and cut out with a cookie cutter. I used both a 2 inch and a 2 1/2 inch cutter.
Bake the cookies in batches, 1 tray at a time. Bake the smaller cookies for 7-8 minutes, and the larger ones for 9-11 minutes, depending on thickness. Your cookies will not brown, they will be pale and soft when done.
Remove the tray from the oven and gently press the flat pansies onto the hot cookies, pressing slightly to adhere the flowers to the cookies. Don't press too hard, the heat of the cookies will do the job. Sprinkle lightly with granulated sugar. Let the cookies cool completely on a rack.
Note: the cookies will be soft when they come out of the oven, but will firm up as they cool.
If you'd like to make these cookies lemony, substitute the sugar for my special citrusy lemon sugar, directions here: How to Make Lemon Sugar. In place of vanilla I use Lemon Paste, or you might use lemon extract.