For the raspberry sauce: Combine the raspberries and sugar in a small saucepan. Bring to a simmer over medium heat and cook for 15 minutes. Add the basil and lime juice and allow the sauce to cool in the fridge.
For the meringue: Combine 1/2 cup water and the rum in a medium saucepan over high heat and bring to a simmer. Slowly stir in 1 cup of the sugar to combine, and use a pastry brush dipped in water to remove any sugar crystals from the side of the pot. Insert a candy thermometer into the mixture.
In the bowl of a stand mixer using a whisk attachment, beat the egg whites on medium speed until foamy. Slowly stream in the remaining 1/2 cup sugar and beat to soft peaks.
When the sugar syrup reaches the soft-ball stage (238 degrees F), remove from the heat. Increase the mixer speed to medium high and slowly stream the sugar syrup into the egg whites in the space between the beaters and the side of the bowl with the mixer running. Continue to beat until the meringue forms soft, glossy peaks.
To assemble the cake: Place the angel food cake onto a cake stand or plate. Pour the raspberry sauce into the center hole. Spread the meringue evenly all over the sides and top of the cake, covering the hole at the top. Use your spatula to create peaks along the tops and sides if desired. Use a kitchen torch to toast the meringue all over before serving.
Propane gas torches are highly flammable and should be kept away from heat, open flame and prolonged exposure to sunlight. They should be used only in well-ventilated areas. Follow torch manufacturer's instructions for use.