Preheat oven to 350 °F. Coat a 13-by-18-inch rimmed baking sheet with cooking spray. Line with parchment or wax paper, leaving a few inches of paper overhanging the ends and coat the paper with cooking spray.
Slowly whisk coffee into 1/3 cup cocoa powder in a medium bowl until smooth. Set aside.
Sift flour, cornstarch, baking powder and salt into another bowl. Set aside.
Beat egg whites in a large bowl with an electric mixer on medium speed until frothy. Increase speed to high and beat until soft peaks form. Add sugar, 1 tablespoon at a time. Continue beating until meringue is glossy and stiff peaks form. Add vanilla.
Whisk 1 cup meringue into reserved cocoa mixture until smooth. Gently fold cocoa mixture into the remaining whites with a rubber spatula until evenly incorporated. Gradually sprinkle the reserved flour mixture over the egg whites, whisking until just incorporated.
Scrape the batter into prepared pan, spreading it into the corners and smoothing the surface. Bake the cake just until top springs back when touched lightly, 10 to 12 minutes. Cool in the pan on a wire rack for 10 minutes. Sift 1 tablespoon cocoa powder over the top of the cake. Turn the cake out onto a fresh sheet of wax paper and sift remaining 1 tablespoon cocoa powder over bottom of the cake. Cover with plastic wrap and chill in the freezer until cold, at least 30 minutes.
Place frozen yogurt in the refrigerator to soften for 30 minutes. (Alternatively, microwave on Low for 30 seconds.)
Coat a 9-by-5-inch loaf pan with cooking spray. Line bottom and sides of pan with plastic wrap, leaving a few inches overhanging the edges. Smooth out any bubbles.
Cut cake into 5-by-9-inch rectangles, using the top of the loaf pan as a guide. Place 1 rectangle in the bottom of the pan, trimming as necessary to fit. Spread half the frozen yogurt in an even layer over the cake. Repeat with the remaining cake and frozen yogurt, ending with a layer of cake. (Reserve any remaining cake for another use.) Wrap the cake with overhanging plastic and then with another layer of plastic wrap. Freeze for at least 4 hours or overnight.
To serve, place the terrine in the refrigerator to soften for 30 minutes. Invert the terrine onto a serving platter or cutting board; remove plastic wrap. With a serrated knife, cut into 12 slices, dipping knife in hot water between slices. Serve with Coffee Creme Anglaise and garnish with raspberries (or chocolate-covered coffee beans).