Blackberry Jam Cake

FOR THE CAKE: Adjust oven rack to lower-middle position and heat oven to 350 degrees. Grease two 9-inch round cake pans, line with parchment paper, grease parchment, and flour pans. Heat cinnamon, allspice, and cloves in small skillet over medium heat until fragrant, about 1 minute; set aside. Microwave jam in bowl until thin enough to pour, 35 to 45 seconds, stirring halfway through microwaving.

 Whisk buttermilk, water, and vanilla into jam. Combine flour, baking powder, salt, and toasted spices in large bowl. Using stand mixer fitted with paddle, beat butter, granulated sugar, and brown sugar on medium-high speed until light and fluffy, about 2 minutes. Reduce speed to medium-low and add eggs, one at a time, until incorporated. Add flour mixture in 3 additions, alternating with jam mixture in 2 additions, stopping occasionally to scrape down bowl.

 Divide batter evenly between prepared pans and smooth tops with rubber spatula. Gently tap pans on counter to release air bubbles. Bake until deep golden brown and toothpick inserted in center comes out clean, 35 to 40 minutes, switching and rotating pans halfway through baking. Let cakes cool in pans on wire rack for 10 minutes. Remove cakes from pans, discarding parchment, and let cool completely on rack, at least 1 hour.

FOR THE FROSTING AND JAM: Whisk sugar, flour, cornstarch, salt, and baking soda together in bowl. Slowly whisk in milk until smooth. Strain mixture through fine-mesh strainer into medium saucepan. Cook over medium heat, whisking constantly, until mixture boils and is very thick, 5 to 7 minutes. Transfer milk mixture to clean bowl and let cool completely, about 2 hours.

 Using stand mixer fitted with whisk attachment, mix cooled milk mixture and vanilla on low speed until combined, about 30 seconds. Add butter, 1 piece at a time, and whip until incorporated, about 2 minutes. Increase speed to medium-high and whip until frosting is light and fluffy, about 5 minutes. Let sit at room temperature until stiff, about 1 hour.

 Whisk jam in bowl until smooth. Line edges of cake platter with 4 strips of parchment to keep platter clean. Place 1 cake layer on platter. Spread 1½ cups frosting evenly over top, right to edge of cake. Spread jam over frosting, leaving ½-inch border. Top with remaining cake layer and spread remaining frosting evenly over top and sides of cake. Press walnuts, if using, onto sides of cake. Refrigerate cake until set, about 30 minutes. Carefully remove parchment strips before serving. (Frosted cake can be refrigerated for up to 24 hours; bring to room temperature before serving.)