Wash and scrub the blood oranges with warm soapy water to remove any wax, then dry the oranges.
Put sugar in a bowl and zest the blood oranges directly into the bowl. Use your fingers to rub the zest into the sugar.
In another bowl, use a citrus reamer to extract juice from the blood oranges. Strain and set aside.
Soak gelatin sheets in a bowl of cold water for 10 minutes to let them bloom.
Combine cream, sugar, and blood orange zest in a small saucepan over medium heat and bring to a simmer. Remove saucepan from heat and set aside.
Lift the gelatin sheets from the cold water and wring gently to remove excess water.
Add the gelatin sheets to the warm cream mixture and stir until they melt completely.
Whisk in the blood orange juice and yogurt until well combined.
Divide the blood orange mixture among six ramekins. Cover and refrigerate for at least 4 hours or overnight for the panna cotta to set.
To make the segmented blood oranges, cut the tops and bottoms off the blood oranges then cut the white pith away from the outside of the fruit.
Cut the wedges of fruit away from the membrane, letting the fruit and juices fall into a prep bowl. Set aside.
To unmold the panna cotta, run a sharp knife around the edges of each ramekin to break the suction, place a serving plate over the top of the ramekin, and invert onto the plate. Garnish with the segmented blood oranges and juice.