Heat oven to 325 degrees F. Grease and flour 10-cup ovenproof bowl.
Sift together flour, 1 cup of the sugar, baking powder and salt into large bowl.
Beat egg whites in small bowl until foamy. Beat in remaining 1/3 cup sugar, 1 tablespoon at a time, until soft peaks form.
Stir 2/3 cup milk, the oil and vanilla into flour mixture; beat at medium speed 1 minute. Add egg yolks and remaining 1/3 cup milk; beat 1 minute. Fold in egg whites until no streaks of white remain. Spoon into prepared 10-cup bowl.
Bake in 325 degree F oven 1 hour 10 minutes or until top springs back when lightly pressed with fingertip. Cool cake in bowl on wire rack 10 minutes. Loosen around edge with thin metal spatula; turn out onto rack; cool completely.
Turn cake, flat side up. With sharp knife, carefully cut cone-shaped piece from center, leaving a cake shell about 1 inch thick. Trim 1/2-inch-thick slice from cone to use for lid; use remainder of cone for snacking.
Beat cream until stiff peaks form. Measure out 1/2 cup of strawberries; fold remaining berries into cream. Spoon cream-strawberry mix into hollow in cake; replace top slice. Carefully flip cake so lid is on bottom and place, rounded side up, on serving plate. Refrigerate.
Beat together butter and 1 cup confectioners sugar in medium-size bowl until smooth and creamy, for about 3 minutes. Mash the reserved 1/2 cup strawberries; beat into butter mixture alternately with 3 cups confectioners sugar until a smooth frosting. Spread a thin layer over cake, about 3/4 cup; reserve remaining frosting.
Beat remaining 1/2 cup confectioners sugar into remaining frosting. Attach star tip to pastry bag; spoon frosting into bag. Pipe into rosettes over cake and around bottom. Chill until serving time. Garnish top with additional strawberries if desired. Cut into wedges to serve. Makes 12 servings.