Preheat the oven to 160°F.
Combine the water and the sugar into a saucepan and let it sit on low heat. Keep stirring the mixture until the sugar dissolves.
When the temperature of the sugar syrup reaches about 230°, place the egg whites in a large mixing bowl and start whisking together with an electric mixer at medium speed.
When the temperature of the sugar syrup reaches about 250°, lower the mixer speed and pour half of the syrup into the egg whites. Increase the speed to medium and whisk the mixture together for a minute. Slowly pour in the remaining syrup, but be careful not to pour it directly over the mixer or else it will make a mess!
Continue whipping until the meringue mixture has cooled. You should be left with a very dense, shiny and smooth meringue. Let this cool before cooking.
Line a baking sheet with parchment paper. Pour the meringue into a piping bag (or you can shape between two spoons) and then squeeze the mixture out onto small rounds, or you can use a shaped nozzle.
Cook the meringue cookies in the oven for 3-4 hours. Turn off the heat, crack the oven slightly, and let the cookies cool in the oven for at least 3 hours, or ideally overnight.
The cookies should be kept in an airtight bag or container, or they can be frozen!