Preheat oven to 225°. In a large bowl, with a mixer (preferably fitted with whisk attachment) on high speed, beat egg whites and cream of tartar until foamy. Gradually add 1 cup sugar, about 1 tbsp. at a time, beating well after each addition and scraping sides of bowl occasionally, until stiff, shiny peaks form (see tip 2 below).
Line 2 baking sheets with baking parchment. Mound meringue in 8 equal portions (a scant 1/2 cup for each) on sheets, spacing at least 3 in. apart. Shape each into a 4-in. bowl-shaped round (follow tip 3 below).
Bake meringues until they sound hollow when tapped and feel firm to the touch, about 1 1/2 hours; switch sheet positions halfway through baking. Turn heat off and leave meringues in closed oven until completely cool, 2 to 2 1/2 hours longer. Remove from sheets.
Set meringues on plates and fill as you like.
Make ahead: Up to 1 day; cool completely, then wrap airtight and store at room temperature.
Tips for perfect meringues:
A whisk attachment introduces air evenly into whites and creates small bubbles, which are both stronger and more flexible than larger ones. Make sure the bowl and beaters are clean; any fat can interfere with the formation of the foam.
Beating the whites with an acid, like cream of tartar or vinegar, helps coagulate the egg-white protein. You want stiff, shiny peaks. The mixture should feel smooth when you rub it between your fingers.
Shape meringue mixture into bowl-shaped rounds with a small, thin spatula. The edges should be a little higher than the centers.