Preheat oven to 350 degrees F (175 degrees C). Grease a 9-inch springform pan with 1 teaspoon butter. Sprinkle 1/2 cup sugar around the bottom the sides of the pan.
Place raspberries in a fine-mesh strainer set over a bowl; press and scrape with a spoon to squeeze out juice. Discards seeds and skins.
Combine raspberry juice, kidney beans, almond meal, eggs, 1/2 cup melted butter, raspberry extract, and almond extract in a food processor; process until smooth.
Pour kidney bean mixture into a large bowl. Mix in 3/4 cup sugar, baking powder, and salt until blended. Pour into the prepared pan.
Bake in the preheated oven until a knife inserted into the center comes out clean, about 40 minutes. Run a sharp knife around the edges of the cake; cool in the pan for 10 to 15 minutes. Remove ring and transfer cake to a serving platter.