Position racks in the upper and lower thirds of the oven; preheat to 250 degrees F. Line 2 baking sheets with parchment paper.
Beat the egg whites, cream of tartar and salt in a large clean dry bowl with a mixer on medium speed until foamy. Increase the speed to medium high and beat until thick and opaque, about 1 more minute. Gradually add the confectioners' sugar, about 1/4 cup at a time, and beat until stiff shiny peaks form, about 5 more minutes.
Scoop 6 large mounds of meringue (3/4 cup each) onto the baking sheets, leaving space between each. Using the back of a spoon, pull up the meringue to form swoops and spikes on each mound. Sprinkle with coarse sugar. Bake at 250 degrees F until dry and crisp, 4 to 5 hours. Let cool completely on the baking sheets. Store in an airtight container in a dry place for up to 1 week.