Craving both cookies and pie? A classic crumb bar is just what you need! It's got a tender, sweet, cookie base; real fruit filling; and toothsome, oaty crumbs on top. It's more portable than pie and more satisfying than a cookie. What to do when your favorite fruit is out of season? Make your way to your supermarket's frozen fruit aisle. Since frozen fruit has been picked at peak ripeness, it's reliably sweet and delicious and often a better value than fresh.
Preheat the oven to 350 degrees F. Butter a 9-inch square baking pan and line it with parchment paper, leaving a 2-inch overhang on two sides. In a large bowl, whisk together the flour, baking powder and salt. In a medium bowl, beat the butter and the brown sugar with an electric mixture on medium speed until fluffy, about 2 minutes. Beat in the egg. Spread about two-thirds of the batter evenly over the bottom of the prepared pan with an offset spatula. Bake the bottom crust until it is golden brown, 24 to 26 minutes. Mix the remaining batter with the oats and set aside.
Meanwhile, in a medium saucepan, combine the apples, raspberries and sugar and cook over medium heat, stirring occasionally, until the mixture is bubbling and the fruit has broken down, 5 to 6 minutes. In a small bowl, mix about 3 tablespoons of the fruit mixture with the cornstarch until smooth. Add the cornstarch mixture to the fruit and simmer for another 2 to 3 minutes. Remove the jam from the heat and let cool slightly.
Top the bottom crust with the fruit and spread it out evenly. Top the fruit with the oat crumb mixture, squeezing it to make some larger clumps. Bake until the top is golden brown, 28 to 32 minutes. Transfer the pan to a rack to cool completely. Using the parchment, lift out the entire bar mixture and place it on a cutting board. Cut into squares.