Make the syrup: In a small saucepan, bring ½ cup water and ½ cup of the sugar to a simmer and cook until the sugar dissolves, 2-3 minutes. Remove from the heat and transfer to a small bowl. Add the lemon juice and zest. Refrigerate.
Caramelize the nuts: Rinse out the pan used to make the syrup and dry well. Add the remaining ¾ cup sugar and enough water for it to look like wet sand. Cook over medium heat until the sugar caramelizes and browns, 5-8 minutes. Add the almonds and carefully stir to coat the nuts with the caramelized sugar. Season with the dry ginger and a pinch salt. Transfer to a baking sheet to cool and harden. When hard, break into bite size pieces.
Assemble the salad: Toss the blackberries, raspberries and apple slices with the lemon syrup in a large bowl. Refrigerate until ready to serve. The colder the fruit, the better. When ready to serve, top with the almond brittle, a ¼ cup scoop of raspberry sorbet and the basil leaves. Serve immediately.