Adjust oven racks to fit two sheet pans in the center of the oven. Line 2 baking sheets with parchment paper. Preheat the oven to 225°F.
Using a stand mixer with the whisk attachment, whip the egg whites and salt on high speed until soft peaks form, about 30 seconds. Reduce speed to medium and very slowly pour in the sugar while the mixer is running. Pour in the blackberry balsamic vinegar and whip until just combined. Stop the mixer and scrape down the sides of the bowl, making sure to scrape the bottom to make sure everything is incorporated evenly. Whip on high speed until the mixture is glossy, stiff, and all the sugar has dissolved, about 30 seconds to 1 minute.
Using a pastry bag fitted with a star tip, pipe meringues onto the baking sheets in 1 ½ inch swirls (the cookies should look similar to icing on the top of a cupcake). Alternatively, use a spoon to dollop the cookies in 1 ½ inch mounds onto the baking sheet. The cookies will not spread, so they may be placed close together on the sheet.
Bake for 1 hour, rotating pans halfway through baking. Turn off the oven and leave the pans inside until the oven and the meringues are completely cool.