Cocoa and brown sugar lend this meringue a denser, moister, creamier texture than usual.
Make the meringue: Preheat oven to 300 degrees. Line a rimmed baking sheet with parchment. Draw an 8-inch circle on parchment, then flip. Mix whites, sugars, and salt in a mixer bowl set over a pan of simmering water. Whisk constantly until sugars dissolve and mixture is warm, about 3 minutes. Remove from heat, and whisk on medium-high speed until stiff peaks form, about 8 minutes. Beat in vanilla.
Sift cocoa powder over meringue, and fold until barely any streaks remain. Using an offset spatula or a large spoon, spread meringue into a round, using circle as a guide. (Be careful not to spread out too much; meringue will spread more during baking.) Form a well in center, being careful not to spread meringue too thin.
Bake meringue until dry to the touch, about 1 hour. Let cool on sheet on wire rack. Meringue will keep, covered, for up to 1 day.
To assemble pavlova: Spread dark-chocolate cream evenly in center of meringue, leaving a 1/2-inch border from edge. Spread whipped cream over chocolate cream. Garnish with chocolate curls, and serve immediately.