Preheat the oven to 400 degrees F. Arrange two oven racks evenly in the oven.
Line a sheet pan with parchment paper and spread the sugar in an even layer on the paper. (Leave a small border of paper around the sugar so the sugar doesn't spill onto the pan.) Bake for 8 to 10 minutes, until the sugar is hot (an edge will begin to brown). Reduce the oven temperature to 250 degrees F.
Meanwhile, place the egg whites in the bowl of an electric mixer fitted with the whisk attachment. When the sugar is almost ready, whisk the egg whites on high speed for 1 minute, until the whites are frothy. With the mixer still on high, slowly add the hot sugar to the egg whites. (I use a large spoon to start and then pick up the paper and pour the sugar in slowly.) Add the vanilla and continue to whisk on high for 10 minutes, until the meringue is at room temperature. It will be very thick and glossy.
Using two large serving spoons, scoop 12 very large oval dollops of meringue onto two sheet pans lined with parchment paper. You should be able to get 6 meringues on each pan; space them well because they will expand while they bake. Place 3 candied rose petals on top of each meringue. Bake for 2 hours, until the outsides of the meringues are crisp and the centers are still soft. Set aside to cool on baking racks. Allow to sit uncovered and serve at room temperature. (Don't refrigerate or store covered or they will lose their crispness.)