Prepare the Crust: Preheat oven to 350°F. Pulse flour, slivered almonds, powdered sugar, and salt in a food processor until thoroughly combined and almonds are finely chopped, 8 to 10 times. Add butter; pulse until mixture resembles coarse meal, 8 or 9 times.

Line bottom and sides of a 13- x 9-inch pan with aluminum foil, allowing 2 to 3 inches to extend over sides; lightly coat foil with cooking spray. Press flour mixture evenly in bottom of prepared pan. Bake in preheated oven until beginning to brown around edges, about 20 minutes. Cool completely on a wire rack, about 20 minutes.

Prepare the Filling: Pulse sliced almonds, granulated sugar, flour, and salt in a food processor until nuts are very finely ground, 10 to 12 times. Add butter, and pulse until fully incorporated, 10 to 12 times. Add eggs and almond extract, and pulse just until mixture is combined, 5 or 6 times. Spread almond mixture evenly over cooled Crust.

Trim rhubarb, and slice into 1 1/2- x 2-inch pieces. Slice in half horizontally, and cut into 1/2-inch-wide strips. Place strips of rhubarb, color side up, and raspberries evenly on top of almond mixture.

Bake at 350°F until a wooden pick inserted into center comes out clean and mixture is golden brown on top, 45 to 50 minutes. Cool completely in pan on a wire rack, about 1 hour. Using aluminum foil as handles, remove bars from pan. Dust with powdered sugar, cut into squares or triangles, and serve.