Orange-Cardamom Butter Cakes with Rose Water Icing

Preheat oven to 325°F. Combine milk, orange zest, and orange blossom water in a small bowl. Split vanilla bean half in half lengthwise, and scrape vanilla seeds into milk mixture; stir to combine. Add vanilla bean pod to milk mixture; set aside. Generously grease bottom and sides of 8 wells of a 12-cup standard muffin pan with butter. Dust generously with flour. Tilt to cover sides completely, and tap out excess. Set aside. 

Whisk together flour, baking powder, cardamom, and salt in a medium bowl. Beat butter and sugar in a large bowl with an electric mixer on medium speed until light and fluffy, 5 to 7 minutes, stopping to scrape sides of bowl as needed. Add eggs to butter mixture, 1 at a time, beating on medium speed until combined and stopping to scrape sides of bowl as needed. Remove vanilla bean pod from milk mixture; discard. With mixer running on low speed, gradually add flour mixture to butter mixture in 3 additions, alternating with milk mixture, beating until batter is smooth, about 2 minutes. Divide batter evenly among 8 prepared wells of muffin pan (about 1/4 cup per well); smooth tops with an offset spatula. 

Bake in preheated oven until a wooden pick inserted in center of cakes comes out clean, 18 to 20 minutes. Let cool in pan 10 minutes. Remove from pan; let cool completely on a wire rack, about 20 minutes. Using a serrated knife, remove and discard domed tops from cakes. Invert cakes, cut sides down, on cutting board. Halve cakes crosswise, creating 2 layers for each.

Beat powdered sugar and butter in a medium bowl with an electric mixer on medium-high speed until light and fluffy, about 5 minutes, stopping to scrape down sides as needed. Add orange blossom water, vanilla extract, and rose water; beat until combined, about 30 seconds. Stir together raspberry jam and orange juice in a small bowl until smooth. 

To assemble cakes, spread 2 teaspoons icing on bottom layer of 1 cake. Top with 1 teaspoon jam mixture, and place top cake layer on jam. Spread a thin layer of icing on outside of cake; spread 2 teaspoons icing on top of cake. Dollop top with 1 teaspoon jam mixture, letting excess gently drip down sides. Repeat with remaining cakes. Garnish with dried rose petals.