Preheat the oven to 400 degrees F. Arrange two racks evenly spaced in the oven.
Line a sheet pan with parchment paper and spread the sugar so it’s a perfectly even thickness on the paper right to the edge of the sugar, leaving a border on the paper so the sugar doesn’t spill onto the pan. Bake for 8 to 10 minutes, until the edges start to brown lightly. Watch carefully! Lower the oven to 250 degrees F.
Meanwhile, place the egg whites in the bowl of an electric mixer fitted with the whisk attachment. Just before the sugar is ready, whisk the egg whites on high speed for one minute, until frothy. With the mixer on low, slowly add the hot sugar to the egg whites. (I use a large spoon at first, 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 egg whites are room temperature. (The bowl may still be warm.) The meringue will be very thick and glossy.
Using two large serving spoons, scoop 6 very large, messy oval dollops of meringue onto each of two sheet pans lined with parchment paper, spacing them out because they will expand while they bake. Sprinkle the pistachios on top and bake for 1 1/2 to 2 hours (make sure your oven isn’t above 250 degrees!), until the outsides of the meringues are crisp but not browned and the centers are still soft. Sprinkle with fleur de sel and set aside to cool.