Preheat oven to 325 degrees. Butter a 9-inch pie plate; set aside. Puree berries and milk in a blender; set aside. Stir together butter, flour, salt, and 1/2 cup plus 2 tablespoons granulated sugar in a medium bowl. Stir in egg yolks, berry mixture, lemon juice, and vanilla.
Beat egg whites until foamy in the bowl of an electric mixer fitted with the whisk attachment. With mixer running, add remaining 2 tablespoons granulated sugar in a steady stream; beat until stiff (but not dry) peaks form. Gently fold whites into strawberry mixture.
Ladle batter into buttered pie plate; place in a roasting pan. Pour boiling water around plate, halfway up sides. Bake until golden, about 35 minutes. (If top browns too quickly, tent with foil.) Let cool on a wire rack 10 minutes. Dust with confectioners' sugar; top with berries.