Preheat oven to 300°. In a food processor, whirl butter, 1/2 cup sugar, grated lemon peel, lemon juice, flour, cornstarch, and basil leaves until smooth.
Press dough into two 8-inch cake pans with removable rims. Press tines of a fork around edges to make a ridge pattern, then pierce dough with fork in parallel lines about an inch apart.
Bake until firm to touch and slightly browned, about 45 minutes (40 in convection oven). Sprinkle hot rounds with 2 tablespoons sugar. Remove pan rims and cut each round, while still warm, into 12 or 16 wedges. Let cool completely on pan bottoms on racks, then remove wedges and serve or store airtight up to 1 week.
Servings Makes 24 or 32 wedges