Blood oranges are used three ways in this dessert: syrup made with fresh juice is brushed onto the cake's layers; chopped sections are tossed with mint as a filling; and whole sections garnish the top of the cake. You can make the layers ahead and keep them frozen for up to 2 months. Thaw at room temperature and then assemble. This cake is best served within 2 hours of assembling.
To prepare cake, coat an 8-inch round cake pan with cooking spray; line bottom of pan with wax paper. Coat wax paper with cooking spray.
Combine eggs, 1/4 teaspoon vanilla, and salt in a large bowl, and beat with a mixer at high speed 2 minutes. Gradually add 1/2 cup granulated sugar, beating until egg mixture is thick and pale (about 3 minutes). Gently fold flour into egg mixture, 1/4 cup at a time. Spoon batter into prepared pan.
Bake at 375° for 20 minutes or until cake springs back when touched lightly in center. Cool in pan 10 minutes on a wire rack; remove from pan. Cool completely on wire rack.
To prepare filling, place a colander in a 2-quart glass measure or medium bowl. Line colander with 4 layers of cheesecloth, allowing cheesecloth to extend over outside edges. Spoon yogurt into colander. Cover loosely with plastic wrap; refrigerate 12 hours.
Spoon yogurt cheese into a large bowl; discard liquid. Add honey and 1/2 teaspoon vanilla to yogurt, stirring well with a whisk.
Combine cream and powdered sugar in a medium bowl, and beat with a mixer at high speed until soft peaks form. Gently stir one-fourth of the cream mixture into yogurt mixture; gently fold in remaining cream mixture. Cover and chill 15 minutes.
Arrange blood orange sections in a single layer on several layers of paper towels, and let stand 5 minutes. Reserve half of the sections; roughly chop remaining sections. Combine chopped orange sections and chopped mint. Cover and chill.
To prepare syrup, combine juice and 1/4 cup granulated sugar in a small saucepan; bring to a boil over medium-high heat, stirring constantly with a whisk. Reduce heat; simmer until reduced to 1/4 cup (about 15 minutes). Remove from heat; cool.
Split cake in half horizontally using a serrated knife; place bottom layer, cut side up, on a plate. Brush with 2 tablespoons syrup. Spread with half of yogurt mixture, leaving a 1/4-inch border. Sprinkle chopped blood orange mixture