- Preheat the oven to 325°F (160°C). Have ready an ungreased 10-inch (25 cm) angel food cake pan.
- For the cake, place the 10 egg whites in a large mixing bowl, or in the bowl of a stand mixer fitted with the whip attachment. Add the cream of tartar and whip on high speed until foamy. With the mixer still running, add 1/4 cup (50 g) of the sugar and continue to whip until medium peaks form when the beaters are lifted. Set aside.
- Sift the flour, the remaining 1 1/4 cups (250 g) of sugar, baking powder and salt into a mixing bowl (if using a stand mixer, you do not need to wash the bowl or whip attachment after whipping the egg whites). Add the lime zest, lime juice, oil and the 7 egg yolks. Whip on medium-low speed for 1 minute and then increase the speed to medium-high, whipping for about 2 minutes, until the batter is smooth.
- Fold the whipped whites into the batter in 2 additions (using a whisk allows you to fold easily without deflating the whipped whites).
- Pour the batter into the tube pan and bake for about 1 hour, until the centre springs back when gently pressed. Cool the cake in the pan, either upside down on a wire rack or, if the pan has “feet,” directly on the counter.
- To make the buttercream, place the egg whites and sugar in a metal bowl and set it over a saucepan filled with 2-inches (5 cm) of gently simmering water. Whisk constantly (but not vigorously) until the mixture reaches 150°F (65°C) on a candy thermometer, about 6 minutes.
- Use electric beaters or transfer the mixture to the bowl of a stand mixer fitted with the whip attachment and whip on high speed until the meringue has cooled to room temperature (it will hold a stiff peak by then).
- With the mixer running on high speed, add the butter a few pieces at a time. At first the meringue will hold its volume, then the buttercream will deflate a little and become very creamy yet fluffy looking. Beat in the raspberry purée, lime juice and vanilla. Set aside.
- When the cake has cooled and you’re ready to assemble it, run a palette knife around the inside edge of the cake pan. Insert a skewer down the inside of the centre hole in a few places, just to loosen the cake a bit. Tap out the cake onto the counter (you may have to tap it quite hard, but it will come out intact).
- assemble the cake, use a serrated knife to slice it horizontally into 3 equal layers. Place the bottom third of the cake on a platter or a cake stand and spread the top of it with buttercream. Use a small palette knife to reach into the centre hole and spread buttercream on the inside ring.
- Set the middle layer on top. Spread buttercream in the centre hole and spread a little buttercream on the edges of both layers of cake. Make sure it is well covered.
- Spread some buttercream on top of the middle layer of cake and then add the top layer, pressing gently to ensure the cake is level.
- Spread some buttercream around the edges of the centre hole and then cover the top and sides of the cake completely. Chill the cake for about an hour to set the buttercream, uncovered, until ready to serve.
- To garnish the cake, make sure the raspberries are dry and at room temperature. Dip half of the raspberries into granulated sugar in a small bowl, shaking off any excess—the sugar will stick to the berries and look like a light coating of frosting. Alternate dusted and undusted berries in a circle on top of the cake, and insert a few mint leaves so the arrangement has the appearance of a wreath.
Make Ahead: You can bake the cake up to 2 days ahead and store it, unfrosted and well-wrapped, at room temperature. The fully assembled cake can be refrigerated for a further 1 to 2 days. Add the berry garnish no more than 4 hours before serving, otherwise the sugar on the berries will dissolve. Store the decorated cake, uncovered, in the fridge until serving time.
Helpful Hint: Use the buttercream at room temperature. When frosting the cake, it’s easiest to spread buttercream inside the centre hole at each layer with a small palette knife, rather than trying to do all 3 layers together once the cake is fully assembled.