Preheat the oven to 350 degrees . In a medium bowl, whisk together the egg whites and sugar until the sugar is dissolved. Whisk in the flour and vanilla, then whisk in the melted butter.
Spoon 2 tablespoons of batter onto each half of a parchment-paper-lined 12-by-16-inch baking sheet. Using the back of a spoon, spread each mound of batter evenly into a 6-inch circle.
Bake the cookies until golden-brown, about 8 minutes; meanwhile, invert 2 small bowls on a work surface. Slide the parchment paper (with the cookies) onto the countertop and let cool for 5 seconds. Working quickly and using a metal spatula, drape the cookie over the inverted bowl to form an upside-down cup. Repeat with the remaining cookie; if the cookie has set, return to the oven for 10 seconds to soften. Repeat with the remaining batter to make 4 more cookies.