Make the Pavlovas: Preheat oven to 200 degrees. Line a baking sheet with parchment paper.
Beat egg whites in the bowl of a mixer on low speed until foamy, 2 to 3 minutes. Add cornstarch and vinegar; whisk on medium speed until soft peaks form, 2 minutes. Gradually whisk in sugar. Raise speed to medium-high and whisk until very stiff, glossy peaks form, 3 to 4 minutes. Whisk in 1 tablespoon poppy seeds.
Using a large spoon, place 25 mounds of the mixture onto parchment paper. Sprinkle with the remaining poppy seeds. Bake until the outsides are firm, about 1 1/2 hours. (The insides should still be marshmallow-soft.) Turn off the oven, and let meringue cool on the baking sheet for at least 2 hours or overnight to prevent excessive cracking. When cool, carefully remove from parchment.
Make the yogurt topping: In the bowl of a mixer fitted with the whisk attachment, beat heavy cream, yogurt, and sugar until stiff peaks form, 4 to 5 minutes. Top each Pavlova with about 1 tablespoon of the yogurt mixture and berries.