Preheat oven to 350 degrees F. Line an 8-inch-square baking pan with foil and generously coat it with cooking spray.Advertisement
To prepare crust: Combine flour, confectioners' sugar, cornstarch and 1/4 teaspoon salt in a medium bowl. Add oil and butter; using your fingertips, blend into the flour mixture until evenly combined. The mixture will be a little crumbly. Firmly press the dough into the prepared pan. Bake until just barely beginning to brown around the edges, 15 to 20 minutes.
To prepare filling: Meanwhile, combine raspberries and water in a medium saucepan. Cook over high heat, stirring frequently, until the fruit is very soft and mostly broken down, 4 to 6 minutes. Pour through a fine-mesh sieve into a medium bowl, pressing on the solids to extract all the liquid. Pour the strained juice into a glass measuring cup. You need 1 cup strained juice; remove any extra or add a little water if you are short. Stir in lemon (or lime) juice.
Whisk granulated sugar, cornstarch and 1/8 teaspoon salt in a medium bowl until well combined. Whisk in eggs. Stir in the juice mixture. Pour the filling over the crust.
Bake until just set, 15 to 20 minutes. (The center should still be a little jiggly--it will firm up as it cools.)
Let cool to room temperature in the pan on a wire rack, about 1 1/2 hours. Gently lift out of the pan all in one piece using the edges of the foil. Cut into 9 squares. Garnish with fresh raspberries and dust with confectioners' sugar, if desired, just before serving.
Make Ahead Tip: Cover and store at room temperature for up to 1 day.
1/2 starch, 1/2 fruit, 1 other carbohydrate, 1 1/2 fat