Preheat oven to 350 ° F. Butter and flour a 10 cup bundt pan. Whisk together flour, baking powder, baking soda, salt, cardamom and cinnamon in a large bowl. Set aside.
Beat the butter until creamy, about 2 minutes. Gradually add sugar and beat until the mixture is light in texture and color, about 3 minutes.
Beat in eggs one at a time, beating well after each addition. Scrape down sides of bowl. Add flour mixture and sour cream in additions.
Scoop about 1/3 of the batter into the pan, smooth with a spatula and sprinkle with some apples. Put the rest of the batter and the apples in layers, smoothing the top.
Bake cake for 50 to 60 minutes, or until a toothpick inserted in the center comes out clean. Cool the cake in the pan on a cooling rack for 10 minutes, then invert it onto the rack. Let cool completely.
To prepare glaze, beat cream cheese and powdered sugar until creamy, about 1 minute. Add orange juice and beat until completely smooth. Pour glaze/icing over the cooled cake.