Bring sliced blood oranges and water to a boil in a medium saucepan. Cover, turn heat to low, and simmer for 20 minutes. Carefully transfer to blender and let cool 10 minutes. Blend on high power until completely smooth. Measure out two cups, and discard (or repurpose - smoothie?) any leftover. There won't be much.
Preheat oven to 350ºF. Grease and flour a 9x2" round baking pan and line the bottom with a circle of parchment paper.
In a large bowl, combine two cups of the blood orange puree with the melted butter and egg. In a separate bowl, whisk together the flour, sugar, baking powder and salt. Pour the orange mixture into the flour mixture and gently fold together with a rubber spatula until just combined.
Bake in centre of oven for about 40 minutes, or until centre feels a bit bouncy when lightly pressed. Let cool a few minutes in pan, then invert onto a cooling rack to cool completely.
To make glaze, whisk together juice and confectioners' sugar. If you prefer a runnier glaze, add a bit of water about a half-teaspoon at a time. Spread or pour over cake once it's completely cool.