Preheat oven to 350°F. Butter 9x9x2-inch metal baking pan; line bottom with parchment paper. Stir bittersweet chocolate, butter, and unsweetened chocolate in small saucepan over low heat until chocolates melt and mixture is smooth. Cool 10 minutes.
Whisk 3/4 cup sugar and eggs in large bowl until well blended, about 1 minute.
Whisk in chocolate mixture. Sift flour, cocoa, baking powder, and salt over; stir to blend.
Transfer batter to prepared pan.
Bake cake until top looks dry and tester inserted into center comes out with some thick sticky batter attached, about 17 minutes. Cool cake in pan to room temperature.
Cut around cake in pan.
Place cutting board over pan and invert, tapping out cake. Peel off parchment. Using 3-inch round cutter, cut out 6 cake rounds (save remaining cake for another use). Line small baking sheet with parchment paper. Arrange cake rounds on prepared sheet. Using 2 1/4- to 2 1/2-inch-diameter ice cream scoop, place scoop of strawberry ice cream in center of each round, leaving about 1/4-inch plain border. Freeze until ice cream is solid, about 2 hours.
Combine remaining 3/4 cup sugar and egg whites in large metal bowl. Set bowl over saucepan of gently simmering water and whisk until mixture is very warm, about 2 minutes.
Remove bowl from over water. Using electric mixer, beat meringue at high speed until very thick and billowy, about 2 minutes.
Place baking sheet with cake rounds on work surface. Mound 2 heaping tablespoons meringue atop ice cream on 1 cake round.
Spread meringue evenly over to cover, sealing meringue to plain cake border and swirling decoratively. Repeat with remaining desserts. Freeze uncovered on baking sheet until meringue is solid, at least 2 hours and up to 2 days.
Preheat oven to 500°F.
Transfer desserts still on baking sheet from freezer directly to oven.
Bake until meringue is deep brown in spots, turning sheet as needed for even cooking, about 3 minutes.
