Because they are less acidic than regular oranges, blood oranges taste a bit sweeter. Reducing the fresh juice concentrates the flavor and makes a stunning ruby-colored sauce. Use regular oranges if you can't find blood oranges. Prepare the cake up to two days in advance
Preheat oven to 325°.
To prepare cake, coat a 10-inch tube pan with cooking spray; dust with 1 tablespoon flour. Set aside.
Lightly spoon 2 1/4 cups flour into dry measuring cups; level with a knife. Combine flour, baking powder, and salt; stir well with a whisk.
Combine 1 1/2 cups sugar, butter, and cheese in a large bowl; beat with a mixer at medium speed until well blended (about 7 minutes). Add rinds; beat well. Add 3 large eggs, 1 at a time, beating well after each addition.
Combine buttermilk, 1/4 cup orange juice, and lemon juice. Add flour mixture and buttermilk mixture alternately to sugar mixture, beginning and ending with flour mixture. Place egg whites in a medium bowl. Beat with a mixer at high speed until soft peaks form, using clean, dry beaters. Add remaining 1/4 cup sugar, 1 tablespoon at a time, beating until stiff peaks form. Gently fold one-third of egg white mixture into batter, and fold in remaining egg white mixture. Spoon batter into prepared pan.
Bake at 325° for 1 hour and 10 minutes or until a wooden pick inserted in center comes out clean. Cool in pan on a wire rack for 10 minutes. Remove cake from pan; cool completely on a wire rack.
To prepare sauce, combine the blood orange juice and 2/3 cup sugar in a large, heavy saucepan; bring to a boil, stirring until sugar dissolves. Reduce heat, and simmer until reduced to 1 cup (about 30 minutes). Serve sauce with cake.