Prepare an 8-inch cake pan by lining the bottom with parchment and greasing the pan all over. Using parchment (especially for this recipe) makes removing the cake from the pan much easier - it will prevent some oranges slices from sticking to the pan and prevent the oranges from getting too brown. Sprinkle granulated sugar where you have greased the pan. This will prevent the cake from sticking and will caramelize the orange slices beautifully.
Thoroughly wash the oranges. With a sharp knife, slice the mandarin oranges into very thin slices, about 1/2cm in thickness. Remove any seeds in orange slices. Do the same with the blood orange.
Using the larger centre pieces of sliced oranges first, line the bottom cake pan. Alternate between mandarin orange and blood orange slices. You will have smaller oranges slices leftover; do not feel like you have to use up all the slices. Once you have finished lining the cake pan, set cake pan aside.
In the bowl of a standing mixer, cream together butter and granulated sugar until pale and fluffy. Add eggs one at a time. Add vanilla. Mix well.
In a medium-sized bowl, whisk together flour, baking powder, and salt.
Alternating between the two, gradually add the dry ingredients and milk to the butter-sugar mixture. Careful not to overmix.
Transfer batter into the prepared cake pan.
Bake for 50 - 55 minutes or until toothpick comes out clean.
Let cake cool for 5 minutes before flipping cake over onto a plate to let cool completely.