Step 1Heat the oven to 350 degrees. Butter six 4-inch individual tart pans with removable bottoms.
Step 2Carefully rinse the blackberries and pat them dry. (Set aside the 12 berries for garnish.) Puree the half pint of berries in a food processor or blender until smooth, then strain the puree through a fine mesh strainer and discard the seeds. Stir 1 tablespoon sugar into the puree and set aside.
Step 3In a large bowl, stir together the flour, cake flour and salt and set aside. In a medium bowl, beat the egg yolks with 2 1/2 tablespoons sugar until thick and lemon-colored. Stir in the lemon zest and vanilla and set aside while beating the egg whites.
Step 4Beat 3 of the egg whites along with the cream of tartar to soft peaks. Gradually beat in 3 tablespoons sugar until stiff peaks form. Quickly fold the beaten egg whites into the beaten egg yolks. Fold in the flour mixture until just combined. Then quickly fold in the melted butter. Divide the mixture evenly among the tart pans and gently smooth the tops.
Step 5Place the tart pans on a baking sheet. Bake about 15 minutes, until the cakes are lightly browned and set in the center. Cool on a wire rack, then remove from the tart pans.
Step 6In a small saucepan, combine one-fourth cup water and the remaining three-fourths cup sugar. Cook over medium heat until the syrup reaches 238 degrees on a candy thermometer. Remove from the heat. Beat the remaining three egg whites to form soft peaks, 30 seconds to 1 minute. With the mixer running at medium speed add the syrup in a slow stream. Continue beating until the meringue is cool and stiff peaks form, about 3 to 5 minutes.
Step 7Place the cakes on a baking sheet. Divide the meringue evenly among the six cakes and spread over the top. The meringue also can be spooned into a pastry bag with a large round tip and piped over the cakes. Place the cakes under the broiler until the edges are golden brown, 1 to 2 minutes. To serve the cakes, garnish each with a couple of fresh blackberries, and drizzle a little blackberry puree around each cake. Serve immediately.