Preheat oven to 325°F. Position racks in center and top of oven. Spray a 9-inch springform pan with baking spray; line bottom with parchment paper. Place pan on a rimmed baking sheet.

Break almond paste up by hand into roughly ½-inch chunks. Process almond paste, granulated sugar, powdered sugar, and pistachios in a food processor until finely ground, about 30 seconds. Add butter, oil, orange blossom water, and almond extract; process until fluffy, about 30 seconds. Add eggs, one at a time, through food chute, pulsing until combined after each addition.

Transfer almond paste mixture to a large bowl. Whisk together flour, baking powder, salt, and cardamom in a medium bowl. Add flour mixture to almond paste mixture; whisk just until combined. Clean food processor.

Spread batter evenly in prepared pan. Bake the cake on the center rack until a wooden pick inserted in center comes out clean, 1 hour and 15 minutes to 1 hour and 20 minutes, placing a sheet of aluminum foil on top rack of oven after 25 minutes to help prevent overbrowning. Let cool in pan on a wire rack 10 minutes. Remove sides of pan; let cool completely on pan base on a wire rack, about 2 hours.

Process sugar, ricotta, cream cheese, orange blossom water, and salt in a food processor until smooth and well combined, about 1 minute. Transfer sugar mixture to a large bowl.

Beat cream in a separate large bowl until stiff peaks form. Gradually fold whipped cream into sugar mixture until combined.

Transfer Torte to a serving plate; generously dust with powdered sugar and garnish with pistachios. Serve with Ricotta Whipped Cream and berries.